Multiplicity of solutions for gradient systems using Landesman-Lazer conditions

DOI10.1155/2010/237826zbMath1207.35126OpenAlexW2149697656WikidataQ58649784 ScholiaQ58649784MaRDI QIDQ1957563

Edcarlos D. Da Silva

Publication date: 27 September 2010

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/225099

zbMATH Keywords

resonanceelliptic systemeigenvalue problem with indefinite weights

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) General topics in linear spectral theory for PDEs (35P05) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational methods for elliptic systems (35J50) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Second-order elliptic systems (35J47)

Related Items (7)

Existence of weak solutions for a class of quasilinear elliptic systems ⋮ Sign-preserving solutions for a class of asymptotically linear systems of second-order ordinary differential equations ⋮ Unnamed Item ⋮ Existence of weak solutions for a class of \((p,q)\)-Laplacian systems on resonance ⋮ Nontrivial solutions of elliptic systems with nonlinearities may not have asymptotic limits ⋮ Gradient systems with sublinear term near the origin and asymptotically linear term near infinity ⋮ Multiplicity of solutions for gradient systems with strong resonance at higher eigenvalues

Cites Work

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• Multiplicity results for some elliptic systems near resonance with a nonprincipal eigenvalue
• Strong uniqueness for second order differential operators
• On the Morse indices of sign changing solutions of nonlinear elliptic problems
• Infinite dimensional Morse theory and multiple solution problems
• An extension of the Hess-Kato theorem to elliptic systems and its applications to multiple solution problems
• Radial symmetry of minimizers for some translation and rotation invariant functionals
• Multiplicity of solutions for resonant elliptic systems
• Uniqueness theorems for second order elliptic differential equations
• Linking theorems and applications to semilinear elliptic problems at resonance
• Strict Monotonicity of Eigenvalues and Unique Continuation
• Critical point theory for asymptotically quadratic functionals and applications to problems with resonance
• Principal eigenvalue for weight matrix in elliptic systems
• Semilinear elliptic boundary value problems with double resonance between two consecutive eigenvalues

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