Three solutions for a strongly resonant elliptic problem

DOI10.1016/0362-546X(94)E0016-AzbMath0821.35052OpenAlexW2074868914MaRDI QIDQ4328324

Olímpio Hiroshi Miyagaki, José Valdo A. Goncalves

Publication date: 3 October 1995

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(94)e0016-a

zbMATH Keywords

Ekeland's variational principlesemilinear Dirichlet problemmountain-pass lemmastrong resonace

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Variational methods for second-order elliptic equations (35J20)

Related Items (12)

Multiplicity results for a quasilinear elliptic equation ⋮ Multiple positive solutions for semilinear elliptic equations in ℝ involving critical exponents ⋮ Compactly supported solutions of Schrödinger equations with small perturbation ⋮ Existence of three nontrivial solutions of an elliptic boundary-value problem with discontinuous nonlinearity in the case of strong resonance ⋮ Three nontrivial solutions for a quasilinear elliptic differential equation at resonance with discontinuous right hand side ⋮ Quasilinear hemivariational inequalities with strong resonance at infinity. ⋮ Multiple solutions for nonlinear elliptic equations at resonance with a nonsmooth potential. ⋮ Small perturbations of Robin problems driven by the \(p\)-Laplacian plus a positive potential ⋮ Multiple positive solutions for semilinear elliptic equations in N involving subcritical exponents ⋮ A multiplicity theorem for problems with the \(p\)-Laplacian ⋮ Nonsmooth critical point theory and nonlinear elliptic equations at resonance ⋮ A critical point theorem for perturbed functionals and low perturbations of differential and nonlocal systems

Cites Work

• Existence of solutions for a class of resonant elliptic problems
• On the variational principle
• Critical point theorems and applications to nonlinear boundary value problems
• Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity
• Non-trivial solutions of elliptic equations at resonance
• Existence of nontrivial solutions of partial differential equations with discontinuous nonlinearities
• Remarks on finding critical points
• Multiple nontrivial solutions of semilinear strongly resonant elliptic equations
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