Nonselfadjoint semilinear elliptic boundary value problems
type: Item
instance of: scholarly article
title: Nonselfadjoint semilinear elliptic boundary value problems
zbMATH Open document ID: 0674.35031
DOI: 10.1007/BF01774291
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1987-01-01T00:00:00Z
review text: The author considers a semilinear elliptic boundary value problem \[ Au=g(x,Du)\quad on\quad \Omega,\quad Bu=0\quad on\quad \partial \Omega \] of order m at resonance, where g is bounded and Du denotes the vector of partial derivatives up to order m-1. The main new feature compared with earlier papers of \textit{H. Shaw} [J. Differ. Equations 26, 335-346 (1977; Zbl 0341.35039)] and the reviewer [ibid. 32, 186-192 (1979; Zbl 0377.35028)] is that no variable in Du is distinguished here, whereas before the main weight has been put on u. The abstract setting applies also to weakly coupled elliptic systems as indicated by examples. Its proof relies on the Leray-Schauder degree.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 47J05
zbMATH DE Number: 4103577
zbMATH Keywords: semilinear
zbMATH Keywords: resonance
zbMATH Keywords: abstract setting
zbMATH Keywords: Leray-Schauder degree
author: Antonio Cañada
reviewed by: Georg Hetzer
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01774291
OpenAlex ID: W2076505385
description: scientific article; zbMATH DE number 4103577