Resonance problems for the \(p\)-Laplacian with a nonlinear boundary condition

DOI10.1016/j.na.2005.07.035zbMath1104.35012OpenAlexW2003451681MaRDI QIDQ2492484

Chun-Lei Tang, Shu-Zhi Song

Publication date: 9 June 2006

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.2005.07.035

zbMATH Keywords

nonlinear boundary condition\(p\)-LaplacianresonanceSobolev trace inequalityLandesman-Lazer type conditionG-link

Mathematics Subject Classification ID

Related Items (14)

Existence of weak solutions for a class of quasilinear elliptic systems ⋮ Existence of solutions for Kirchhoff type problems with resonance at higher eigenvalues ⋮ Existence of solutions for a nonlinear problem at resonance ⋮ Existence of weak solutions for a class of \((p,q)\)-Laplacian systems on resonance ⋮ Existence of solutions for Dirichlet problems with \(p\)-Laplacian ⋮ Existence results for the \(p(x)\)-Laplacian with nonlinear boundary condition ⋮ Resonance problems for the \(p\)-Laplacian systems ⋮ Nonexistence, existence and multiplicity of positive solutions to the \(p(x)\)-Laplacian nonlinear Neumann boundary value problem ⋮ Multiple positive solutions for a class of semilinear elliptic systems with nonlinear boundary condition ⋮ Positive solutions of elliptic equations with nonlinear boundary conditions ⋮ A local mountain pass theorem and applications to a double perturbed \(p(x)\)-Laplacian equations ⋮ Existence of nontrivial solution for a nonlocal elliptic equation with nonlinear boundary condition ⋮ Solutions and multiple solutions for \(p(x)\)-Laplacian equations with nonlinear boundary condition ⋮ Resonance problems for \((p,q)\)-Laplacian systems

Cites Work

• Critical point theory and Hamiltonian systems
• Existence of positive solutions of a semilinear elliptic equation in \(\mathbb{R}_+^n\) with a nonlinear boundary condition
• Solvability of the forced Duffing equation at resonance
• Solvability for two-point boundary value problems
• Linking and existence results for perturbations of the \(p\)-Laplacian
• Isolation and simplicity for the first eigenvalue of the \(p\)-Laplacian with a nonlinear boundary condition
• Resonance problems for \(p\)-Laplacian
• Resonance problems for the \(p\)-Laplacian
• Existence and non-existence results for a quasilinear problem with nonlinear boundary condition
• Strong resonance for some quasilinear elliptic equations
• Landesman-lazer conditions and quasilinear elliptic equations
• Resonance problems for the one-dimensional $p$-Laplacian
• Solvability of Neumann problem for elliptic equations at resonance
• Remarks on multiple nontrivial solutions for quasi-linear resonant problems
• Existence results for the \(p\)-Laplacian with nonlinear boundary conditions
• Some existence theorems for elliptic resonant problems.
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