Fucik spectrum, sign-changing, and multiple solutions for semilinear elliptic boundary-value problems with resonance at inifinity
type: Item
instance of: scholarly article
title: Fucik spectrum, sign-changing, and multiple solutions for semilinear elliptic boundary-value problems with resonance at inifinity
zbMATH Open document ID: 0974.35028
author: E. N. Dancer
author: Zhitao Zhang
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-12-18T00:00:00Z
review text: The Fučik spectrum and the theory of ordinary differential operators in Banach spaces are used to study semilinear elliptic boundary-value problems with jumping nonlinearities with zero or infinities, especially resonances of infinity. Results for the existence of multiple solutions and sign-changing solutions are obtained.
reviewed by: Niels Jacob
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35P99
zbMATH DE Number: 1542458
zbMATH Keywords: semilinear elliptic boundary-value problems
zbMATH Keywords: Fučik spectrum
zbMATH Keywords: resonances
zbMATH Keywords: critical point theory
zbMATH Keywords: jumping nonlinearity
MaRDI profile type: Publication
full work available at URL: jmaa.2000.6969
OpenAlex ID: W1991569327
cites work: Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
cites work: A Note on Degree Theory for Gradient Mappings
cites work: On the existence of sign changing solutions for semilinear Dirichlet problems
cites work: Multiple Solutions for a Nonlinear Dirichlet Problem
cites work: A sign-changing solution for a superlinear Dirichlet problem
cites work: Q4379844
cites work: Q3876715
cites work: Q3333437
cites work: Infinite dimensional Morse theory and multiple solution problems
cites work: Remarks on multiple solutions for asymptotically linear elliptic boundary value problems
cites work: Q4224944
cites work: Existence of changing sign solutions for some semilinear problems with jumping nonlinearities at zero
cites work: Multiple solutions of some semilinear elliptic equations via the generalized Conley index
cites work: On sign-changing solutions of certain semilinear elliptic problems
cites work: Variational and topological methods in partially ordered Hilbert spaces
cites work: Multiple solutions theorems for semilinear elliptic boundary value problems with resonance at infinity
cites work: Fucik spectrum, sign-changing and multiple solutions for semilinear elliptic boundary value problems with jumping nonlinearities at zero and infinity.
cites work: Q4778359
cites work: Q4322681
cites work: Critical point theory and Hamiltonian systems
cites work: Q5773424
cites work: Computation of critical groups in Fučík resonance problems.
cites work: Double resonance problems with respect to the Fucik spectrum
cites work: Q4850189
cites work: Q4320200
cites work: Q3247607
DOI: 10.1006/JMAA.2000.6969
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description: scientific article; zbMATH DE number 1542458