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