Non-trivial solutions of elliptic equations at resonance

DOI10.1017/S0308210500011732zbMath0431.35040MaRDI QIDQ3868165

Klaus Thews

Publication date: 1980

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

nonlinear Dirichlet problemsLusternik-Schnirelmann theoryproblems at resonanceconditions of Landesman-Lazer typeexistence of multiple nontrivial solutions

Mathematics Subject Classification ID

Related Items (37)

Periodic solutions of dynamical systems ⋮ Multiplicity of solutions for resonant Neumann problems with an indefinite and unbounded potential ⋮ Remarks on a resonant problem with an unbounded nonlinearity ⋮ Existence and multiplicity of solutions for Neumann problems ⋮ Splitting subspaces and saddle points ⋮ Asymptotically linear elliptic equations with resonance at infinity ⋮ Three nontrivial solutions for a quasilinear elliptic differential equation at resonance with discontinuous right hand side ⋮ Nonlinear elliptic boundary value problems at resonance ⋮ Pairs of nontrivial smooth solutions for nonlinear Neumann problems ⋮ On global dynamics of reaction-diffusion systems at resonance ⋮ Nonlinear hemivariational inequalities at resonance ⋮ Three solutions for a strongly resonant elliptic problem ⋮ Unnamed Item ⋮ T-periodic solutions of time dependent Hamiltonian systems with a potential vanishing at infinity ⋮ Resonant Robin problems driven by the p-Laplacian plus an indefinite potential ⋮ The Hampwile theorem for nonlinear eigenvalues ⋮ Nontrivial solutions for a multivalued problem with strong resonance ⋮ Quasilinear hemivariational inequalities with strong resonance at infinity. ⋮ An existence theorem for nonlinear hemivariational inequalities at resonance ⋮ Nonlinear hemivariational inequalities at resonance ⋮ Asymptotically linear elliptic problems at resonance ⋮ On a critical point theorem and an application to a nonresonance problem between two eigenvalues of the \(p\)-Laplacian ⋮ Multiple solutions for strongly resonant nonlinear elliptic problems with discontinuities ⋮ A Bounded Mountain Pass Lemma Without the (PS) Condition and Applications ⋮ The palais-smale condition versus coercivity ⋮ Existence and multiplicity of solutions for second order periodic systems with the \(p\)-Laplacian and a nonsmooth potential ⋮ Qualitative phenomena for some classes of quasilinear elliptic equations with multiple resonance ⋮ Nonlinear Neumann problems with indefinite potential and concave terms ⋮ The mountain pass alternative ⋮ On a resonant elliptic problem with singular terms ⋮ Nonsmooth critical point theory and nonlinear elliptic equations at resonance ⋮ Multiple solutions of semilinear elliptic problems in a ball ⋮ Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity ⋮ Resonant Neumann problems with indefinite and unbounded potential ⋮ Nonlinear problems with strong resonance at infinity: an abstract theorem and applications ⋮ Asymptotically linear elliptic boundary value problems ⋮ Periodic solutions of asymptotically linear systems without symmetry

Cites Work

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• Multiple solutions for elliptic boundary value problems with odd nonlinearities
• Dual variational methods in critical point theory and applications
• Stability of critical points under small perturbations. I: Topological theory

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