On the number and structure of solutions for a Fredholm alternative with the \(p\)-Laplacian.

DOI10.1006/jdeq.2002.4173zbMath1247.35052OpenAlexW2042522114MaRDI QIDQ1864637

Peter Takáč

Publication date: 18 March 2003

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.2002.4173

zbMATH Keywords

nonlinear eigenvalue problem\(p\)-LaplacianFredholm alternativeglobal minimizerquasilinear Dirichlet problemdegenerate or singularsecond-order Taylor formula.

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) Boundary value problems for second-order elliptic equations (35J25) Degenerate elliptic equations (35J70) Weak solutions to PDEs (35D30) Blow-up in context of PDEs (35B44) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (7)

Measure of noncompactness, surjectivity of gradient operators and an application to the \(p\)-Laplacian ⋮ On the Fredholm alternative for the \(p\)-Laplacian at higher eigenvalues (in one dimension) ⋮ A variational approach to the Fredholm alternative for the \(p\)-Laplacian near the first eigenvalue ⋮ Poincaré inequality and Palais-Smale condition for the \(p\)-Laplacian ⋮ Dirichlet problems for the \(p\)-Laplacian with a convection term ⋮ Solvability of the resonant 1-dimensional periodic \(p\)-Laplacian equations ⋮ On compactness conditions for the \(p\)-Laplacian

Cites Work

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• Regularity for a more general class of quasilinear equations
• Existence and localization of solution for second order elliptic BVP in presence of lower and upper solutions without any order
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• On maximum principles and existence of positive solutions for some cooperative elliptic systems
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• On The Dirichletproblem for Quasilinear Equations
• Boundary regularity for solutions of degenerate elliptic equations
• Nonexistence of Solutions and an Anti-Maximum Principle for Cooperative Systems with thep-Laplacian
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• Generic Fredholm alternative-type results for the one dimensional \(p\)-Laplacian.
• Fredholm alternative for the \(p\)-Laplacian in higher dimensions
• Variational problems with a \(p\)-homogeneous energy
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