Poincaré inequality and Palais-Smale condition for the \(p\)-Laplacian

DOI10.1007/S00526-006-0055-8zbMath1134.35034OpenAlexW2047017253MaRDI QIDQ873142

Pavel Drábek, Peter Takáč

Publication date: 28 March 2007

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-006-0055-8

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) A priori estimates in context of PDEs (35B45) Variational methods for second-order elliptic equations (35J20)

Related Items (4)

Improved Friedrichs inequality for a subhomogeneous embedding ⋮ Superlinear critical resonant problems with small forcing term ⋮ Solvability of the resonant 1-dimensional periodic \(p\)-Laplacian equations ⋮ On compactness conditions for the \(p\)-Laplacian

Cites Work

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• The Fredholm alternative at the first eigenvalue for the one dimensional \(p\)-Laplacian
• An improved Poincaré inequality and the \(p\)-Laplacian at resonance for \(p>2\)
• On the number and structure of solutions for a Fredholm alternative with the \(p\)-Laplacian.
• Bounded perturbations of homogeneous quasilinear operators using bifurcations from infinity
• Resonance problems for the \(p\)-Laplacian
• A strong maximum principle for some quasilinear elliptic equations
• On the Fredholm Alternative for the p -Laplacian in One Dimension
• On the Equation div( | ∇u | p-2 ∇u) + λ | u | p-2 u = 0
• C1 + α local regularity of weak solutions of degenerate elliptic equations
• 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
• 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.
• Fredholm alternative for the \(p\)-Laplacian in higher dimensions

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