Existence and multiplicity for a resonance problem for the \(p\)-Laplacian on bounded domains in \(\mathbb R^N\)

DOI10.1016/J.NA.2008.02.003zbMath1159.35368OpenAlexW1980143141MaRDI QIDQ2518845

Gabriel López Garza, Adolfo J. Rumbos

Publication date: 20 January 2009

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.2008.02.003

zbMATH Keywords

critical groupsMorse index\(p\)-LaplacianresonanceLandesman-Lazer condition

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear elliptic equations (35J60)

Related Items (5)

On a resonance problem with the discrete \(p\)-Laplacian on finite graphs ⋮ Applications of Morse theory to some nonlinear elliptic equations with resonance at zero ⋮ Some bifurcation results and multiple solutions for the \(p\)-Laplacian equation ⋮ Critical point theory to isotropic discrete boundary value problems on weighted finite graphs ⋮ Critical groups at zero and multiple solutions for a quasilinear elliptic equation

Cites Work

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• Marino-Prodi perturbation type results and Morse indices of minimax critical points for a class of functionals in Banach spaces
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• Resonance problems for the \(p\)-Laplacian
• Landesman-lazer conditions and quasilinear elliptic equations
• On the Equation div( | ∇u | p-2 ∇u) + λ | u | p-2 u = 0
• Multiple solutions of semilinear elliptic problems at resonance
• Nontrivial Solutions forp-Laplace Equations with Right-Hand Side Havingp-Linear Growth at Infinity
• Remarks on multiple nontrivial solutions for quasi-linear resonant problems
• Morse index estimates for continuous functionals associated with quasilinear elliptic equations.

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