On existence and multiplicity of solutions of Neumann boundary value problems for quasi-linear elliptic equations

DOI10.1016/j.na.2005.10.010zbMath1109.35047OpenAlexW2011522638MaRDI QIDQ2498792

Xian Wu, Kok-Keong Tan

Publication date: 16 August 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.2005.10.010

zbMATH Keywords

critical point\(p\)-LaplacianNeumann problemSobolev's embedding

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear elliptic equations (35J60) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Applications of operator theory to differential and integral equations (47N20)

Related Items (19)

Existence of multiple solutions with precise sign information for superlinear Neumann problems ⋮ Landesman-lazer type \((p, q)\)-equations with Neumann condition ⋮ Existence of three nontrivial smooth solutions for nonlinear resonant Neumann problems driven by the \(p\)-Laplacian ⋮ Response Solutions for Quasi-Periodically Forced, Dissipative Wave Equations ⋮ The existence and multiplicity of solutions for \(p(x)\)-Laplacian-like Neumann problems ⋮ Existence and multiplicity of solutions for p-Laplacian Neumann problems ⋮ A multiplicity theorem for the Neumann \(p\)-Laplacian with an asymmetric nonsmooth potential ⋮ Sign-changing and extremal constant-sign solutions of nonlinear elliptic Neumann boundary value problems ⋮ Existence of solutions for quasilinear elliptic equations with jumping nonlinearities under the Neumann boundary condition ⋮ A \(p\)-Laplacian supercritical Neumann problem ⋮ Solutions for Neumann boundary value problems involving \(p(x)\)-Laplace operators ⋮ Multiple solutions for superlinear \(p\)-Laplacian Neumann problems ⋮ Linking solutions for \(p\)-Laplace equations with nonlinear boundary conditions and indefinite weight ⋮ Existence of three nontrivial solutions for nonlinear Neumann hemivariational inequalities ⋮ The existence of two nontrivial solutions via homological local linking for the non-coercive \(p\)-Laplacian Neumann problem ⋮ Multiple solutions for nonlinear Neumann problems driven by a nonhomogeneous differential operator ⋮ Applications of local linking to nonlocal Neumann problems ⋮ Nontrivial solutions for a class of resonant \(p\)-Laplacian Neumann problems ⋮ Infinitely many sign-changing solutions for \(p\)-Laplacian Neumann problems with indefinite weight

Cites Work

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• Existence of multiple solutions of critical quasilinear elliptic Neumann problems
• On a three critical points theorem
• Elliptic partial differential equations of second order
• Existence of infinitely many weak solutions for a Neumann problem
• INFINITELY MANY SOLUTIONS OF THE NEUMANN PROBLEM FOR ELLIPTIC EQUATIONS INVOLVING THE p-LAPLACIAN
• Remarks on finding critical points
• Perturbations of second order linear elliptic problems by unbounded nonlinearities
• On the solvability of a nonlinear second-order elliptic equation at resonance
• Solvability of Neumann problem for elliptic equations at resonance

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