Multiplicity of nontrivial solutions of semilinear elliptic equations

DOI10.1006/jmaa.2000.6704zbMath0964.35051OpenAlexW1995311545MaRDI QIDQ1587426

Shui-Qiang Liu, Chun-Lei Tang, Xing-Ping Wu

Publication date: 2 July 2001

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.2000.6704

zbMATH Keywords

critical pointnontrivial solutionsemilinear elliptic equationDirichlet boundary value problemreduction method

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear boundary value problems for linear elliptic equations (35J65) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38)

Related Items (8)

Nontrivial solutions of semilinear equations at resonance ⋮ On multiplicity of solutions of Dirichlet problem for uniformly elliptic operator equations ⋮ Remarks on multiple solutions for elliptic resonant problems ⋮ Existence of positive solutions of elliptic mixed boundary value problem ⋮ Multiplicity results for semilinear resonant elliptic problems with discontinuous nonlinearities ⋮ Existence of multiple nontrivial solutions for semilinear elliptic problems ⋮ A multiplicity result for semilinear resonant elliptic problems with nonsmooth potential ⋮ Multiplicity results for semilinear elliptic problems with resonance

Cites Work

• Saddle points and multiple solutions of differential equations
• Critical point theory and the number of solutions of a nonlinear Dirichlet problem
• Multiplicity results for semilinear elliptic problems at resonance and with jumping nonlinearities
• Nontrivial solutions for a strongly resonant problem
• On an elliptic boundary value problem at double resonance
• Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity
• A reduction method for some nonlinear dirichlet problems
• Remarks on finding critical points

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