Some results for semilinear differential equations at resonance
type: Item
instance of: scholarly article
title: Some results for semilinear differential equations at resonance
zbMATH Open document ID: 0531.47039
DOI: 10.1016/0022-247X(83)90193-2
author: Song-Sun Lin
published in: Journal of Mathematical Analysis and Applications
publication date: 1983-01-01T00:00:00Z
review text: The author considers the problem of the existence of a solution of a so- called resonance problem that is, for an equation of the type \[ (1)\quad Au=F(x,u)\quad in\quad \Omega, \] where the linear (differential) operator A is self-adjoint with a nontrivial kernel on \(L_ 2(\Omega)\) and the nonlinear map F(x,\(\xi)\) satisfies some growth conditions for large values of \(| \xi |\). This paper is written in the spirit of the approach of the paper of \textit{E. M. Landesman} and \textit{A. C. Lazer}, J. Math. Mech. 19, 609-623 (1970; Zbl 0193.392).
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 47H05
zbMATH DE Number: 3842560
zbMATH Keywords: semilinear differential equations at resonance
zbMATH Keywords: eigenvalues
zbMATH Keywords: kernel
zbMATH Keywords: resonance problem
reviewed by: Michael Th. Rassias
MaRDI profile type: Publication
cites work: Q5588800
cites work: Q4167193
cites work: Q3314437
cites work: Some applications of monotone operator theory to resonance problems
cites work: Q3733621
cites work: Nonlinear mappings of monotone type in Banach spaces
description: scientific article; zbMATH DE number 3842560