On the Fredholm alternative for the \(p\)-Laplacian at higher eigenvalues (in one dimension)

DOI10.1016/j.na.2009.11.048zbMath1206.34030OpenAlexW2094352321MaRDI QIDQ847359

Jiří Benedikt, Peter Takáč, Petr Girg

Publication date: 12 February 2010

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.2009.11.048

zbMATH Keywords

nonlinear eigenvalue problemFredholm alternativePrüfer's transformationone-dimensional \(p\)-Laplacianquasilinear Dirichlet problem

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Singular nonlinear boundary value problems for ordinary differential equations (34B16) Boundary eigenvalue problems for ordinary differential equations (34B09)

Related Items (4)

\(p\)-trigonometric and \(p\)-hyperbolic functions in complex domain ⋮ Dirichlet problems for the \(p\)-Laplacian with a convection term ⋮ Perturbation of the \(p\)-Laplacian by vanishing nonlinearities (in one dimension) ⋮ A class of multi-parameter eigenvalue problems for perturbed \(p\)-Laplacians

Cites Work

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• On the Nature of the Spectrum of Singular Second Order Linear Differential Equations
• Generic Fredholm alternative-type results for the one dimensional \(p\)-Laplacian.
• Fredholm alternative for the \(p\)-Laplacian in higher dimensions

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