Existence of non-spurious solutions to discrete Dirichlet problems with lower and upper solutions

DOI10.1016/j.na.2006.07.010zbMath1130.39017OpenAlexW1980665030MaRDI QIDQ884507

Christopher C. Tisdell, Irena Rachůnková

Publication date: 6 June 2007

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2006.07.010

zbMATH Keywords

convergencesecond-order difference equationdiscrete Dirichlet boundary value problem

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Discrete version of topics in analysis (39A12)

Related Items (28)

Positive solutions of a discrete second-order boundary value problems with fully nonlinear term ⋮ Existence of sign-changing periodic solutions of second order difference equations ⋮ Constant-sign solutions for a nonlinear Neumann problem involving the discrete p-Laplacian ⋮ Singular discrete and continuous mixed boundary value problems ⋮ Existence of non-spurious solutions to discrete fourth-order Lidstone boundary value problems ⋮ Discrete approaches to continuous boundary value problems: existence and convergence of solutions ⋮ Existence of positive solutions to discrete second-order boundary value problems with indefinite weight ⋮ Three solutions for a discrete nonlinear Neumann problem involving the \(p\)-Laplacian ⋮ Nontrivial solutions for discrete boundary value problems with multiple resonance via computations of the critical groups ⋮ Nonspurious solutions of the Dirichlet problem for the prescribed mean curvature spacelike equation in a Friedmann-Lemaître-Robertson-Walker spacetime ⋮ Global diffeomorphism theorem applied to the solvability of discrete and continuous boundary value problems ⋮ Two Positive Solutions for a Nonlinear Neumann Problem Involving the Discrete p-Laplacian ⋮ Existence and uniqueness of positive solution for discrete multipoint boundary value problems ⋮ Global structure of positive solutions of a discrete problem with sign-changing weight ⋮ ASYMPTOTIC INTEGRATION OF SECOND-ORDER NONLINEAR DIFFERENCE EQUATIONS ⋮ Bifurcation from infinity and multiple solutions for some discrete Sturm-Liouville problems ⋮ Non-trivial solutions for a discrete nonlinear boundary value problem with $phi_c$-Laplacian ⋮ Unbounded perturbations of nonlinear second-order difference equations at resonance ⋮ Nonlinear discrete periodic boundary value problems at resonance ⋮ Non-spurious solutions to discrete boundary value problems through variational methods ⋮ Unbounded perturbations of nonlinear discrete periodic problem at resonance ⋮ Global structure of sign-changing solutions for discrete Dirichlet problems ⋮ Global structure of positive solutions for superlinear discrete boundary value problems ⋮ Bifurcation interval for positive solutions to discrete second-order boundary value problems ⋮ A global description of the positive solutions of sublinear second-order discrete boundary value problems ⋮ Spectrum of discrete second-order difference operator with sign-changing weight and its applications ⋮ Discrete Dirichlet boundary value problems with upper semicontinuous right-hand sides ⋮ Existence of a priori bounded solutions for discrete two-point boundary value problems

Cites Work

• On multipoint boundary value problems for discrete equations
• The uniqueness of solutions to discrete, vector, two-point boundary value problems
• Systems of difference equations associated with boundary value problems for second order systems of ordinary differential equations
• Topological methods for some boundary value problems
• Existence of multiple solutions for second-order discrete boundary value problems
• Boundary value problems for systems of difference equations associated with systems of second-order ordinary differential equations
• The nonexistence of spurious solutions to discrete, two-point boundary value problems
• Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations
• Difference Equations Associated with Boundary Value Problems for Second Order Nonlinear Ordinary Differential Equations
• A discrete boundary value problem
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