Solvability of the resonant 1-dimensional periodic \(p\)-Laplacian equations

DOI10.1016/J.JMAA.2010.04.070zbMath1204.34022OpenAlexW2015888351MaRDI QIDQ984768

Yong Wang, Mei Yue Jiang

Publication date: 20 July 2010

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2010.04.070

zbMATH Keywords

periodic solutionsFredholm alternative\(p\)-Laplacian equation

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Periodic solutions to ordinary differential equations (34C25) Boundary eigenvalue problems for ordinary differential equations (34B09)

Related Items (6)

Existence and multiple solutions for higher order difference Dirichlet boundary value problems ⋮ Perturbation of the \(p\)-Laplacian by vanishing nonlinearities (in one dimension) ⋮ Multiplicity of periodic solutions for a higher order difference equation ⋮ Existence of homoclinic orbits for a higher order difference system ⋮ Solutions and multiple solutions for superlinear perturbations of the periodic scalar p-Laplacian ⋮ Existence of periodic solutions for higher order difference equations containing both many advances and retardations

Cites Work

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• The Fredholm alternative for the one-dimensional \(p\)-Laplacian
• Poincaré inequality and Palais-Smale condition for the \(p\)-Laplacian
• Periodic solutions of some resonant Hamiltonian systems
• Symplectic transformations and periodic solutions of Hamiltonian systems
• The Fredholm alternative at the first eigenvalue for the one dimensional \(p\)-Laplacian
• The Conley index and the critical groups via an extension of Gromoll-Meyer theory
• Infinite dimensional Morse theory and multiple solution problems
• On the number and structure of solutions for a Fredholm alternative with the \(p\)-Laplacian.
• Critical groups computations on a class of Sobolev Banach spaces via Morse index
• A Landesman-Lazer type theorem for periodic solutions of the resonant asymmetric \(p\)-Laplacian equation
• A strong resonance problem
• On the Fredholm Alternative for the p -Laplacian in One Dimension
• On the Fredholm alternative for the $p$-Laplacian
• On the Fredholm alternative for the p-Laplacian at the first eigenvalue
• The Fredholm alternative for the p-Laplacian: Bifurcation from infinity, existence and multiplicity
• Generic Fredholm alternative-type results for the one dimensional \(p\)-Laplacian.
• Nontrivial periodic solutions for asymptotically linear Hamiltonian systems with resonance
• Fredholm alternative for the \(p\)-Laplacian in higher dimensions

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