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Lectures on Linear Algebra and its Applications. In the
series De Gruyter Textbook, Walter de Gruyter, Oct 24, 2023 -
Mathematics - 258 pages. ISBN: 9783111085401.
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Chapters 1-5 provide a textbook for the course ``Linear Algebra" for sophomores in science and engineering. Chapter 6 has in depth presentation of systems of differential equations. Chapter 7 has applications to Mathematical Analysis and Differential Geometry. The book has many interesting exercises, and detailed hints are given. This book is well suited for self-study, or for a refresher course, as well as a regular textbook. An extensive solution manual, written by the author, is available. The publisher lets university libraries buy E-books, which makes them free to students. Please consider adapting this book. |
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Lectures on Differential Equations. AMS/MAA Textbooks 54,
MAA Press, Providence, RI, 2019. xii+399 pp. ISBN: 978-1-4704-5173-8
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Chapters 1-4 provide a textbook for the course ``Differential Equations" for sophomores in science and engineering. Chapters 7 and 8 cover the course ``Fourier Series and PDE". Chapters 5 and 6 are suitable for a graduate ODE course. An extensive solution manual, written by the author, is available. The publisher lets university libraries buy E-books, which makes them free to students. Please consider adapting this book. |
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Solutions Manual for "Lectures on Differential Equations" 195 pp.
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available in pdf |
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Global solution curves for semilinear elliptic equations.
World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2012. xii+241
pp. ISBN: 978-981-4374-34-7; 981-4374-34-2
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Please ask your library to order a hard copy, or write to the author |
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Necessary and sufficient condition for existence for a case of eigenvalues of multiplicity two.
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Electron. J. Differential Equations 2024, Paper No. 09.
available in pdf |
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Periodic and unbounded solutions of periodic systems
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Bull. Malays. Math. Sci. Soc. 47 (2024), no. 4, Paper No. 107.
available in pdf |
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Infinitely many solutions for a class of resonant problems
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NoDEA Nonlinear Differential Equations Appl. 30 (2023), no. 4, Paper No. 48, 17 pp.
available in pdf |
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Generalized Pohozhaev's identity for radial solutions of $p$-Laplace equations
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Georgian Math. J. 30 (2023), no. 2, 263267.
available in pdf |
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Iterative solution of elliptic equations
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with D. Schmidt Electron. J. Qual. Theory Differ. Equ. 2022, No. 34, 1-9. available in pdf |
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Infinitely many solutions and asymptotics for resonant oscillatory problems
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with D. Schmidt Special issue in honor of Alan C. Lazer, Electron. J. Diff. Equ., Special Issue 01, 301-313 (2021). available in pdf |
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Non-singular solutions of $p$-Laplace problems, allowing multiple changes of sign in the nonlinearity
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Electron. Res. Arch. 30 (2022), no. 4, 1414-1418.
available in pdf |
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Continuation of global solution curves using global parameters
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with D. Schmidt J. Comput. Appl. Math. 440 (2024), Paper No. 115621, 18 pp. available in pdf |
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Calculating Global Solution Curves for Boundary Value Problems
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with D. Schmidt From the Wolfram Notebook Archive (2022) available: https://notebookarchive.org/2022-07-9pt96oa |
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Solving partial differential equations on balls in R^n
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with D. Schmidt From the Wolfram Notebook Archive (2021) available: https://notebookarchive.org/2021-08-cgkai6z |
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On the interaction of species capable of explosive growth
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Applied Mathematics and Nonlinear Sciences, Sciendo (2021), 1-10.
available in pdf |
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Global solution curves in harmonic parameters, and multiplicity of solutions
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Journal of Differential Equations 296 (2021), 186-212.
available in pdf |
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A remark on Pinney's equation
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Communications on Applied Nonlinear Analysis 26 (2019), no 4, 98 - 100.
available in pdf |
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Global solution curves for first order periodic problems, with applications
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with D. Schmidt Nonlinear Anal. Real World Appl. 56 (2020), 103161, 18 pp. available in pdf |
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Infinitely many solutions and Morse index for non-autonomous elliptic problems
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Commun. Pure Appl. Anal. 19 (2020), no. 1, 31-46.
available in pdf |
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A computer assisted study of uniqueness of nodal ground state solutions
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with Y. Li and D. Schmidt J. Comput. Appl. Math. 356 (2019), 402406. available in pdf |
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Bounded solutions for a class of Hamiltonian systems
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with G. Peng Electronic Journal of Qualitative Theory of Differential Equations (2018), No. 81, 1-7. available in pdf |
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A simplified proof of a conjecture for the perturbed Gelfand equation from combustion theory
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with Y. Li and T. Ouyang J. Differential Equations 263 (2017), no. 5, 28742885. available in pdf |
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On separated solutions of logistic population equation with harvesting
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J. Math. Analysis and Applic. 455 (2017), no. 2, 2024-2029. available in pdf |
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Exact multiplicity of solutions for some semilinear Dirichlet problems
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Applicable Anal. 98 (2019), no. 8, 14831495. available in pdf |
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Explicit solutions and multiplicity results for some equations with the $p$-Laplacian
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Quart. Appl. Math. 75 (2017), no. 4, 635-647. available in pdf |
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Global solution curves for several classes of singular periodic problems
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Nonlinear Anal. Real World Appl. 34 (2017), 116. available in pdf |
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A periodic model for the dynamics of cell volume
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Annales Polonici Mathematici 116, no. 3 (2016), 243-249. available in pdf |
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Infinitely many solutions for three classes of self-similar
equations with p-Laplace operator: Gelfand, JosephLundgren and MEMS
problems
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Proc. Roy. Soc. Edinburgh Sect. A 148 (2018), no. 2, 341-356. available in pdf |
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Nonlinear elliptic equations and systems with linear part at resonance
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Electron. J. Diff. Equ., Vol. 2016 (2016), No. 67, pp. 1-17. available in pdf |
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Non-singular solutions of two-point problems, with multiple changes of sign in the nonlinearity
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Proc. Amer. Math. Soc. 144 (2016), no. 6, 25392546. available in pdf |
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Families of solution curves for some non-autonomous problems
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Acta Applicandae Mathematicae (2016) 143(1), 165-178. available in pdf |
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Regularization of radial solutions of $p$-Laplace equations, and computations using infinite series
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Electron. J. Qual. Theory Differ. Equ. (2015), No. 40. available in pdf |
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A global solution curve for a class of free boundary value problems arising in plasma physics
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Appl. Math. Optim. 71 (2015), no. 1, 25-38. available in pdf |
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Harmonic oscillators at resonance, perturbed by a non-linear friction force
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with Y. Li Acta Math. Sci. Ser. B Engl. Ed. 34 (2014), no. 4, 1025-1028. available in pdf |
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Global solution curves for self-similar equations
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J. Differential Equations 257 (2014), no. 7, 2543-2564. available in pdf |
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Exact multiplicity of positive solutions for concave-convex and convex-concave nonlinearities
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with Y. Li J. Differential Equations 257 (2014), no. 10, 37303737. available in pdf |
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A global solution curve for a class of periodic problems, including the relativistic pendulum
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Appl. Anal. 93 (2014), no. 1, 124-136. available in pdf |
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Curves of equiharmonic solutions, and problems at resonance
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Discrete Contin. Dyn. Syst. 34 (2014), no. 7, 2847-2860. available in pdf |
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Non-existence of solutions for non-autonomous elliptic systems of Hamiltonian type
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Comm. Appl. Nonlinear Anal. 21 (2014), no. 3, 13-20. available in pdf |
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Exact multiplicity and numerical computation of solutions
for two classes of non-autonomous problems with concave-convex
nonlinearities
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Nonlinear Anal. 93 (2013), 226235. available in pdf |
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Direction of bifurcation for some non-autonomous problems
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Electron. J. Differential Equations 2012, No. 214, 13 pp. available in pdf |
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Nonlinear perturbations of linear elliptic systems at resonance
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Proc. Amer. Math. Soc. 140 (2012), no. 7, 2447-2451. available in pdf |
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A computer assisted study of uniqueness of ground state solutions
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with Y. Li J. Comput. Appl. Math. 236 (2012), no. 11, 2838-2843. available in pdf |
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Existence and uniqueness of solutions for a class of p-Laplace equations on a ball
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Adv. Nonlinear Stud. 11 (2011), no. 4, 875-888. available in pdf |
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Curves of equiharmonic solutions and solvability of elliptic systems
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Differential Integral Equations 24 (2011), no. 11-12, 1147-1162. available in pdf |
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Remarks on time map for quasilinear equations
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with T. Adamowicz J. Math. Anal. Appl. 376 (2011), no. 2, 686-695. available in pdf |
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Global solution curves for a class of quasilinear boundary-value problems
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with Y. Li Proc. Roy. Soc. Edinburgh Sect. A 140 (2010), no. 6, 1197-1215. available in pdf |
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Global solution curves for a class of elliptic systems
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Appl. Anal. 89 (2010), no. 6, 849-860. available in pdf |
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Pohozaev's identity and non-existence of solutions for elliptic systems
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Comm. Appl. Nonlinear Anal. 17 (2010), no. 4, 81-88. available in pdf |
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Computing the location and the direction of bifurcation for sign changing solutions
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with Y. Li Differ. Equ. Appl. 2 (2010), no. 1, 1-13. available in pdf |
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Curves of equiharmonic solutions, and ranges of nonlinear equations
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Adv. Differential Equations 14 (2009), no. 9-10, 963-984. available in pdf |
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Global solution curves for boundary value problems, with linear part at resonance
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Nonlinear Anal. 71 (2009), no. 7-8, 2456-2467. available in pdf |
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An oscillatory bifurcation from infinity, and from zero
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NoDEA Nonlinear Differential Equations Appl. 15 (2008), no. 3, 335-345. available in pdf |
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A global approach to ground state solutions
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Electron. J. Differential Equations 2008, No. 122, 13 pp. available in pdf |
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An exact multiplicity result for a class of symmetric problems
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Port. Math. 65 (2008), no. 2, 257-260. available in pdf |
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Uniqueness and exact multiplicity of solutions for a class of Dirichlet problems
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J. Differential Equations 244 (2008), no. 10, 2602-2613. available in pdf |
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A global solution curve for a class of periodic problems, including the pendulum equation
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Z. Angew. Math. Phys. 58 (2007), no. 5, 749766. available in pdf |
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Stability and instability of solutions of semilinear problems
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Appl. Anal. 86 (2007), no. 2, 135-147. available in pdf |
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On the direction of pitchfork bifurcation
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with X. Hou and Y. Li Proceedings of the Sixth Mississippi StateUBA Conference on Differential Equations and Computational Simulations, 153158, Electron. J. Differ. Equ. Conf., 15, Southwest Texas State Univ., San Marcos, TX, 2007. available in pdf |
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Computation of radial solutions of semilinear equations
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Electron. J. Qual. Theory Differ. Equ. 2007, No. 13, 14 pp. available in pdf |
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Global solution branches and exact multiplicity of solutions for two point boundary value problems
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Handbook of differential equations: ordinary differential equations. Vol. III, 547606, Handb. Differ. Equ., Elsevier/North-Holland, Amsterdam, 2006. available in pdf |
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Positivity for the linearized problem for semilinear equations
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with T. Ouyang Topol. Methods Nonlinear Anal. 28 (2006), no. 1, 5360. available in pdf |
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On the oscillations of the solution curve for a class of semilinear equations
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with A. Galstyan and Y. Li J. Math. Anal. Appl. 321 (2006), no. 2, 576-588. available in pdf |
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Uniqueness and exact multiplicity of solutions for non-autonomous Dirichlet problems
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Adv. Nonlinear Stud. 6 (2006), no. 3, 461-481. available in pdf |
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Existence and uniqueness of solutions for a class of non-autonomous Dirichlet problems
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Funkcial. Ekvac. 48 (2005), no. 1, 99-111. available in pdf |
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On a principle of predatory exclusion
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Appl. Anal. 84 (2005), no. 7, 707-712. available in pdf |
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Application of generalized averages to uniqueness of solutions, and to a non-local problem
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Comm. Appl. Nonlinear Anal. 12 (2005), no. 4, 6978. available in pdf |
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Computing the location and the direction of bifurcation
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with Y. Li and T. Ouyang Mathematical Research Letters 12, 933944 (2005). available in pdf |
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On Lane-Emden type systems
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with J. Shi Discrete Contin. Dyn. Syst. 2005, suppl., 510-517. available in pdf |
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Further remarks on the non-degeneracy condition
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Results Math. 45 (2004), no. 3-4, 293-298. available in pdf |
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Uniqueness and exact multiplicity of solutions for a class of fourth-order semilinear problems
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Proc. Roy. Soc. Edinburgh Sect. A 134 (2004), no. 1, 179-190. available in pdf |
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Curves of positive solutions for supercritical problems
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Appl. Anal. 82 (2003), no. 1, 45-54. available in pdf |
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Perturbation of global solution curves for semilinear problems
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with Y. Li and T. Ouyang Adv. Nonlinear Stud. 3 (2003), no. 2, 289299. available in pdf |
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An accurate computation of the global solution curve for the Gelfand problem through a two point approximation
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Appl. Math. Comput. 139 (2003), no. 2-3, 363369. available in pdf |
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Similarity of solution branches for two-point semilinear problems
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Proceedings of the Fifth Mississippi State Conference on Differential Equations and Computational Simulations (Mississippi State, MS, 2001), 187191 (electronic), Electron. J. Differ. Equ. Conf., 10, Southwest Texas State Univ., San Marcos, TX, 2003. available in pdf |
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A remark on the non-degeneracy condition
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Results Math. 41 (2002), no. 3-4, 334-336. available in pdf |
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Global solution curves for semilinear systems
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Math. Methods Appl. Sci. 25 (2002), no. 1, 3-20. available in pdf |
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Curves of sign-changing solutions for semilinear equations
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Nonlinear Anal. 51 (2002), no. 5, Ser. A: Theory Methods, 801820. available in pdf |
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On uniqueness of positive solutions for a class of semilinear equations
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Discrete Contin. Dyn. Syst. 8 (2002), no. 4, 865-871. available in pdf |
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Stability and Morse indices of solutions for two classes of semilinear problems
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Comm. Appl. Nonlinear Anal. 9 (2002), no. 2, 117. available in pdf |
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Exact multiplicity of solutions for a class of semilinear Neumann problems
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Comm. Appl. Nonlinear Anal. 9 (2002), no. 4, 117. available in pdf |
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The global solution set for a class of semilinear problems
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Differential equations and control theory (Athens, OH, 2000), 177192, Lecture Notes in Pure and Appl. Math., 225, Dekker, New York, 2002. available in pdf |
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New exact multiplicity results with an application to a population model
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with J. Shi Proc. Roy. Soc. Edinburgh Sect. A 131 (2001), no. 5, 1167-1182. available in pdf |
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On the multiplicity of solutions of semilinear equations
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Math. Nachr. 229 (2001), 119-127. available in pdf |
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Monotone approximations of unstable solutions
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J. Comput. Appl. Math. 136 (2001), no. 1-2, 309-315. available in pdf |
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Instability and exact multiplicity of solutions of semilinear equations
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with J. Shi Proceedings of the Conference on Nonlinear Differential Equations (Coral Gables, FL, 1999), 311322 (electronic), Electron. J. Differ. Equ. Conf., 5, Southwest Texas State Univ., San Marcos, TX, 2000. available in pdf |
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Infinitely many solutions at a resonance
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with Y. Li Proceedings of the Conference on Nonlinear Differential Equations (Coral Gables, FL, 1999), 105111 (electronic), Electron. J. Differ. Equ. Conf., 5, Southwest Texas State Univ., San Marcos, TX, 2000. available in pdf |
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Bounded solution to a differential equation (Problem Proposal-1577)
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Mathematical Magazine (?) (2000). available in pdf |
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A pedagogically correct way to square it out
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Amer. J. Math. Management Sci. 20 (2000), no. 3-4, 227228. available in pdf |
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On the exactness of an S-shaped bifurcation curve
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with Y. Li Proc. Amer. Math. Soc. 127 (1999), no. 4, 1011-1020. available in pdf |
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Generalized averages for solutions of two-point Dirichlet problems
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with Y. Li J. Math. Anal. Appl. 239 (1999), no. 2, 478-484. available in pdf |
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Multiplicity and Morse indices of sign-changing solutions for semilinear equations
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with T. Ouyang Canad. Appl. Math. Quart. 7 (1999), no. 3, 239250. available in pdf |
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Multiplicity of positive solutions for semilinear equations on circular domains
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Comm. Appl. Nonlinear Anal. 6 (1999), no. 3, 1735. available in pdf |
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Exact multiplicity of positive solutions for a class of semilinear equations on a ball
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Electron. J. Qual. Theory Differ. Equ. 1999, No. 8, 15 pp. (electronic). available in pdf |
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Uniqueness and exact multiplicity results for two classes of semilinear problems
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Nonlinear Anal. 31 (1998), no. 7, 849865. available in pdf |
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Remarks on Nagumo's condition
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Portugal. Math. 55 (1998), no. 1, 1-9. available in pdf |
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A global solution curve for a class of semilinear equations
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Proceedings of the Third Mississippi State Conference on Difference Equations and Computational Simulations (Mississippi State, MS, 1997), 119127 (electronic), Electron. J. Differ. Equ. Conf., 1, Southwest Texas State Univ., San Marcos, TX, 1998. available in pdf |
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Steady states and long time behavior of some convective reaction-diffusion equations
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Funkcial. Ekvac. 40 (1997), no. 2, 165-183. available in pdf |
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Solution curves for semilinear equations on a ball
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Proc. Amer. Math. Soc. 125 (1997), no. 7, 1997-2005. available in pdf |
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On homoclinic and heteroclinic orbits for Hamiltonian systems
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with A. Lazer and Y. Li Differential Integral Equations 10 (1997), no. 2, 357-368. available in pdf |
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An exact multiplicity result for a class of semilinear equations
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with Y. Li and T. Ouyang Comm. Partial Differential Equations 22 (1997), no. 3-4, 661684. available in pdf |
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Average Temperature in a Reaction-Diffusion Process (Problem Proposal 97-8)
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SIAM Review (1997). available in pdf |
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Exact multiplicity results for boundary value problems with nonlinearities generalising cubic
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with Y. Li and T. Ouyang Proc. Roy. Soc. Edinburgh Sect. A 126 (1996), no. 3, 599-616. available in pdf |
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Solution curves for two classes of boundary-value problems
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with T. Ouyang Nonlinear Anal. 27 (1996), no. 9, 10311047. available in pdf |
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Multiplicity results for two classes of boundary-value problems
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with T. Ouyang SIAM J. Math. Anal. 26 (1995), no. 1, 180-189. available in pdf |
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Exact multiplicity results for a class of boundary-value problems with cubic nonlinearities
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with T. Ouyang J. Math. Anal. Appl. 194 (1995), no. 1, 328341. available in pdf |
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Exact multiplicity results for two classes of periodic equations
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with T. Ouyang J. Math. Anal. Appl. 194 (1995), no. 3, 763779. available in pdf |
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Symmetry of positive solutions for elliptic problems in one dimension
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Appl. Anal. 58 (1995), no. 3-4, 351-365. available in pdf |
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On computation of solution curves for semilinear elliptic problems
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with T. Ouyang Numer. Funct. Anal. Optim. 16 (1995), no. 1-2, 219231. available in pdf |
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Review of "An Introduction to Partial Differential Equations" by M. Renardy and R.C. Rogers
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SIAM Review 37 (1995), no. 5, 469-470. available in pdf |
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Periodic solutions of a differential equation (Problem Proposal 95-9)
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SIAM Review (1995). available in pdf |
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Homoclinic orbits for a class of symmetric Hamiltonian systems
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with A. Lazer Electron. J. Differential Equations 1994, No. 01, approx. 10 pp. (electronic only). available in pdf |
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On the dynamics of two classes of periodic ecological models
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Oscillations in nonlinear systems: applications and numerical aspects. J. Comput. Appl. Math. 52 (1994), no. 1-3, 267275. available in pdf |
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Exact multiplicity results for two classes of boundary value problems
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with T. Ouyang Differential Integral Equations 6 (1993), no. 6, 1507-1517. available in pdf |
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An algorithm for computing unstable solutions of semilinear boundary value problems
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Computing 51 (1993), no. 3-4, 327-334. available in pdf |
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On periodic solutions for singular perturbation problems
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Proc. Roy. Soc. Edinburgh Sect. A 120 (1992), no. 1-2, 143-152. available in pdf |
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Some new results on the periodic competition model
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J. Math. Anal. Appl. 171 (1992), no. 1, 131-138. available in pdf |
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On computation of solutions of fully nonlinear elliptic problems
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with G. Choudury J. Comput. Appl. Math. 41 (1992), no. 3, 301-311. available in pdf |
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Dynamics of the Lotka-Volterra systems with diffusion
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Appl. Anal. 44 (1992), no. 3-4, 191-207. available in pdf |
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A computer-assisted study of periodic parabolic systems
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Appl. Math. Comput. 50 (1992), no. 2-3, 203-221. available in pdf |
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Approximating optimal controls for elliptic obstacle problem by monotone iteration schemes
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with V. Barbu Numer. Funct. Anal. Optim. 12 (1991), no. 5-6, 429-442. available in pdf |
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Computation of solutions of nonlinear boundary value problems
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with G. Choudury Comput. Math. Appl. 22 (1991), no. 8, 49-55. available in pdf |
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An upper bound (Problem Proposal 91-8)
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SIAM Review (1991). available in pdf |
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Monotone iterations for nonlinear obstacle problem
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with A. Leung and S. Stojanovic J. Austral. Math. Soc. Ser. B 31 (1990), no. 3, 259-276. available in pdf |
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On nonlinear singular perturbation problems
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Nonlinear Anal. 15 (1990), no. 5, 467478. available in pdf |
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On existence of periodic solutions for a class of quasilinear noncoercive problems
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Funkcial. Ekvac. 33 (1990), no. 1, 127138. available in pdf |
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On existence of solutions for two classes of nonlinear problems
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Comm. Partial Differential Equations 14 (1989), no. 4, 519539. available in pdf |
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On existence of solutions for a class of fully nonlinear noncoercive problems
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J. Math. Anal. Appl. 137 (1989), no. 2, 477484. available in pdf |
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A maximum principle for fourth order ordinary differential equations
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Appl. Anal. 33 (1989), no. 3-4, 267-273. available in pdf |
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On computation of solutions of elliptic systems
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Numer. Funct. Anal. Optim. 10 (1989), no. 9-10, 977-990. available in pdf |
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On existence of solutions for several classes of free boundary problems
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SIAM J. Math. Anal. 19 (1988), no. 4, 814823. available in pdf |
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On blow up of solutions of nonlinear evolution equations
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Proc. Amer. Math. Soc. 103 (1988), no. 1, 189-197. available in pdf |
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Computation of displacements for nonlinear elastic beam models using monotone iterations
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Internat. J. Math. Math. Sci. 11 (1988), no. 1, 121128. available in pdf |
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On the existence and uniqueness of positive steady states in the Volterra-Lotka ecological models with diffusion
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with A. Leung Appl. Anal. 26 (1987), no. 2, 145-160. available in pdf |
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Existence of solutions for a class of semilinear noncoercive problems
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Nonlinear Anal. 10 (1986), no. 12, 14711476. available in pdf |
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Existence and approximation of solutions of inverse-positive problems
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Nonlinear Anal. 10 (1986), no. 9, 863872. available in pdf |
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A general monotone scheme for elliptic systems with applications to ecological models
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with A. Leung Proc. Roy. Soc. Edinburgh Sect. A 102 (1986), no. 3-4, 315-325. available in pdf |
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On application of the monotone iteration scheme to noncoercive elliptic and hyperbolic problems
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Nonlinear Anal. 8 (1984), no. 2, 97105. available in pdf |
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Existence of periodic solutions for a class of nonlinear problems
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Nonlinear Anal. 7 (1983), no. 8, 873879. available in pdf |
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Existence of solutions for a class of nonlinear noncoercive problems
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Comm. Partial Differential Equations 8 (1983), no. 8, 819846. available in pdf |