Positive solutions of semilinear elliptic equations with small perturbations

DOI10.1090/S0002-9939-2012-11569-2zbMath1266.35081MaRDI QIDQ4911835

Ryuji Kajikiya

Publication date: 20 March 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

perturbation problempositive solutionvariational methodsemilinear elliptic equationmountain pass lemma

Mathematics Subject Classification ID

Perturbations in context of PDEs (35B20) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61) Positive solutions to PDEs (35B09)

Related Items

Existence of positive solutions to semilinear elliptic problems with nonlinear boundary condition ⋮ Small perturbations of an indefinite elliptic equation ⋮ Positive solutions of an elliptic Neumann problem with a sublinear indefinite nonlinearity ⋮ Existence of solution to Kirchhoff type problem with gradient nonlinearity and a perturbation term ⋮ Compactly supported solutions of Schrödinger equations with small perturbation ⋮ Positive solutions for a nonlocal problem with a convection term and small perturbations ⋮ A convergence result for mountain pass periodic solutions of perturbed Hamiltonian systems ⋮ Multiplicity and asymptotic behavior of solutions for quasilinear elliptic equations with small perturbations ⋮ Small perturbations of Robin problems driven by the \(p\)-Laplacian plus a positive potential ⋮ Positivity results for indefinite sublinear elliptic problems via a continuity argument ⋮ A curve of positive solutions for an indefinite sublinear Dirichlet problem ⋮ A critical point theorem for perturbed functionals and low perturbations of differential and nonlocal systems

Cites Work

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• Mountain pass theorem in ordered Banach spaces and its applications to semilinear elliptic equations
• On semilinear elliptic equations with indefinite nonlinearities
• The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function.
• Mountain pass theorem in order intervals and multiple solutions for semilinear elliptic Dirichlet problems
• Minimax theorems
• Dual variational methods in critical point theory and applications
• Positive mountain pass solutions for a semilinear elliptic equation with a sign-changing weight function

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