Resonance problems with respect to the Fucík spectrum

DOI10.1090/S0002-9947-00-02655-6zbMath0951.35049OpenAlexW1990879973MaRDI QIDQ4485734

Schechter, Martin

Publication date: 18 June 2000

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-00-02655-6

zbMATH Keywords

existence of solutionnonlinear perturbationFučík spectrumselfadjoint operator with compact inverseasymptotic resonance

Mathematics Subject Classification ID

Variational inequalities (49J40) Variational methods involving nonlinear operators (47J30) 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)

Related Items (16)

Computation of critical groups in Fučík resonance problems. ⋮ New Linking Theorem and Sign-Changing Solutions ⋮ Sign-changing solutions for some nonlinear problems with strong resonance ⋮ Resonance with respect to the Fučík spectrum for non-selfadjoint operators ⋮ Planar Hamiltonian systems at resonance: the Ahmad-Lazer-Paul condition ⋮ Mountain pass and linking type sign-changing solutions for nonlinear problems involving the fractional Laplacian ⋮ The Fučík spectrum of Schrödinger operator and the existence of four solutions of Schrödinger equations with jumping nonlinearities ⋮ Fučik spectrum for the Kirchhoff-type problem and applications ⋮ The Fučík spectrum of Schrödinger operators in strongly indefinite cases ⋮ Nonresonance conditions on the potential with respect to the Fučík spectrum for semilinear Dirichlet problems ⋮ Double linking theorem and multiple solutions. ⋮ Existence of type (II) regions and convexity and concavity of potential functionals corresponding to jumping nonlinear problems ⋮ Sign-changing solutions for a class of nonlinear elliptic problems ⋮ The Fucik spectrum and critical groups ⋮ THE QUANTITATIVE ANALYSIS ON THE FUCÍK SPECTRUM AND SOLVABILITY OF JUMPING NONLINEAR PROBLEMS ⋮ Sign-changing critical points from linking type theorems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On nontrivial solutions of a Dirichlet problem whose jumping nonlinearity crosses a multiple eigenvalue
• New linking theorems
• On nonlinear elliptic problems with jumping nonlinearities
• Asymptotically linear elliptic boundary value problems
• On the first curve of the Fučik spectrum of an elliptic operator
• Existence results for resonant perturbations of the Fučik spectrum
• Semilinear elliptic problem with crossing of multiple eigenvalues
• On solvability of equations of the $4$th order with jumping nonlinearities
• Critical point theory and boundary value problems with nonlinearities crossing multiple eigenvalues II
• Corrigendum: On the Dirichlet problem for weakly non-linear elliptic partial differential equations
• Résultats d'existence et de non-existence pour certains problèmes demi-linéaires à l'infini
• A variational approach to nonresonance with respect to the Fučik spectrum
• Boundary value problems with jumping nonlinearities

This page was built for publication: Resonance problems with respect to the Fucík spectrum