The Fucik spectrum and critical groups

DOI10.1090/S0002-9939-01-05968-8zbMath0964.35054OpenAlexW1865246195MaRDI QIDQ2719004

Perera, Kanishka, Schechter, Martin

Publication date: 14 May 2001

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-01-05968-8

zbMATH Keywords

critical groupsMorse theoryvariational methodsjumping nonlinearitiesFučik spectrumsemilinear elliptic PDE

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Existence theories for problems in abstract spaces (49J27)

Related Items (14)

Computation of critical groups in Fučík resonance problems. ⋮ New Linking Theorem and Sign-Changing Solutions ⋮ Nonlinear four-point problem: non-resonance with respect to the Fučík spectrum ⋮ \((p,2)\)-equations asymmetric at both zero and infinity ⋮ Basis properties of Fučik eigenfunctions ⋮ The ∞-Fucík spectrum ⋮ Double linking theorem and multiple solutions. ⋮ Sign-changing solutions for a class of nonlinear elliptic problems ⋮ Multiple solutions for a class of semilinear elliptic problems with Robin boundary condition ⋮ Some remarks on the Fučík spectrum of the \(p\)-Laplacian and critical groups ⋮ Critical groups and multiple solutions of the \(p\)-Laplacian equations ⋮ Multiple solutions for semilinear elliptic equations with Neumann boundary condition and jumping nonlinearities ⋮ On the role played by the Fučík spectrum in the determination of critical groups in elliptic problems where the asymptotic limits may not exist ⋮ Morse theory applied to semilinear problems

Cites Work

• Unnamed Item
• Type II regions between curves of the Fučik spectrum and critical groups
• Type (II) regions between curves of the Fučik spectrum
• A generalization of the Amann-Zehnder theorem to nonresonance problems with jumping nonlinearities
• Multiple solutions of asymptotically homogeneous problems
• Résultats d'existence et de non-existence pour certains problèmes demi-linéaires à l'infini
• Resonance problems with respect to the Fucík spectrum

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