On variational methods for nonlinear difference equations

DOI10.1016/j.cam.2009.11.044zbMath1187.39006OpenAlexW2082772631MaRDI QIDQ848555

Marek Galewski, Joanna Smejda

Publication date: 4 March 2010

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2009.11.044

zbMATH Keywords

Morse theoryPalais-Smale conditioncritical pointmonotone operatorboundary value problemfinite-dimensional variational problem

Mathematics Subject Classification ID

Existence theories for free problems in two or more independent variables (49J10) Additive difference equations (39A10) Discrete version of topics in analysis (39A12)

Related Items (15)

Existence of solutions for \(p\)-Laplacian discrete equations ⋮ Multiplicity results on discrete boundary value problems with double resonance via variational methods ⋮ Constant sign solutions for parameter-dependent superlinear second-order difference equations ⋮ Sign-changing diagonal perturbations of Laplacian matrices of graphs ⋮ Existence of solutions for a nonlinear algebraic system with a parameter ⋮ Algebraic systems with Lipschitz perturbations ⋮ Superlinear discrete problems ⋮ Multiple and sign-changing solutions for discrete Robin boundary value problem with parameter dependence ⋮ Landesman–Lazer conditions for difference equations involving sublinear perturbations ⋮ Boundary value problems of a discrete generalized beam equation via variational methods ⋮ Some remarks on nonlinear discrete boundary value problems ⋮ Exponential number of stationary solutions for Nagumo equations on graphs ⋮ Nonuniqueness of implicit lattice Nagumo equation. ⋮ Anti-periodic solutions of higher order nonlinear difference equations: a variational approach ⋮ Variational methods and implicit discrete Nagumo equation

Cites Work

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• Existence of non-zero solutions for a nonlinear system with a parameter
• Existence theorems of periodic solutions for second-order nonlinear difference equations
• Minimax theorems
• Existence results for a nonlinear system with a parameter
• Multiple positive solutions of singular discrete \(p\)-Laplacian problems via variational methods
• Existence of solutions for a nonlinear system with a parameter
• Existence results for discrete Sturm–Liouville problem via variational methods
• The existence of solutions for second-order difference equations
• On variational methods for periodic discrete problems
• Remarks on multiple nontrivial solutions for quasi-linear resonant problems

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