A multiplicity theorem for problems with the \(p\)-Laplacian

DOI10.1016/j.na.2006.12.002zbMath1149.35042OpenAlexW2017293899MaRDI QIDQ5920430

Nikolaos S. Papageorgiou, Motreanu, Dumitru, Viorica V. Motreanu

Publication date: 13 February 2008

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.2006.12.002

zbMATH Keywords

\(p\)-Laplacianelliptic boundary value problemdegree mapmultiple nontrivial solutionsoperator of type \((S)_{+}\)

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear elliptic equations (35J60) Second-order elliptic equations (35J15)

Related Items (9)

Multiple equilibrium points in global attractors for some p-Laplacian equations ⋮ Exact multiplicity of positive solutions for a \(p\)-Laplacian equation with positive convex nonlinearity ⋮ The existence of multiple equilibrium points in a global attractor for some \(p\)-Laplacian equation ⋮ Multiple constant sign and nodal solutions for nonlinear elliptic equations with the \(p\)-Laplacian ⋮ Stationary solutions and connecting orbits for \(p\)-Laplace equation ⋮ Existence of at least five solutions for a differential inclusion problem involving the \(p(x)\)-Laplacian ⋮ Multiple solutions for the \(p\)-Laplacian problem with supercritical exponent ⋮ Multiple positive solutions for a \((p,q)\)-Laplace equation involving singular and critical terms ⋮ A concentration phenomenon for \(p\)-Laplacian equation

Cites Work

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• On the antimaximum principle for the \(p\)-Laplacian with indefinite weight
• Multiplicity results for semilinear elliptic problems at resonance and with jumping nonlinearities
• Asymptotically linear elliptic equations without nonresonance conditions
• On the convergence of solutions of multivalued parabolic equations and applications
• Multiple solutions for nonlinear elliptic equations at resonance with a nonsmooth potential.
• Fucik spectrum, sign-changing, and multiple solutions for semilinear elliptic boundary-value problems with resonance at inifinity
• Positive solution for \(-\Delta_ p u=f(x,u)\) with \(f(x,u)\) growing as \(u^{p-1}\) at infinity.
• Sign-changing and multiple solutions for the \(p\)-Laplacian
• A strong maximum principle for some quasilinear elliptic equations
• A degree theoretic approach for multiple solutions of constant sign for nonlinear elliptic equations
• Linear and quasilinear elliptic equations
• MULTIPLE SOLUTIONS TO p-LAPLACIAN PROBLEMS WITH ASYMPTOTIC NONLINEARITY AS up−1 AT INFINITY
• Fixed point theory and nonlinear problems
• Boundary regularity for solutions of degenerate elliptic equations
• A Note on Degree Theory for Gradient Mappings
• Existence of multiple solutions for quasilinear and semilinear elliptic equations
• Applying the mountain pass theorem to an asymptotically linear elliptic equation on R^N
• Generalizations of Browder's Degree Theory
• Three solutions for a strongly resonant elliptic problem
• Multiple solutions of semilinear elliptic problems at resonance
• Asymptotically linear Dirichlet problem for the \(p\)-Laplacian
• Remarks on multiple nontrivial solutions for quasi-linear resonant problems
• Variational and topological methods for Dirichlet problems with \(p\)-Laplacian

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