General existence theorems for quasilinear elliptic systems without monotonicity
type: Item
instance of: scholarly article
title: General existence theorems for quasilinear elliptic systems without monotonicity
zbMATH Open document ID: 0688.35023
DOI: 10.1016/0022-247X(90)90428-I
author: Hong Thai Nguyen
author: Jürgen Appell
author: Peter P. Zabreĭko
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: Existence theorems for quasilinear elliptic systems \(Lu(x)=f(x,u(x))\) and \(Lu(x)=g(x,u(x),Vu(x)),\) subject to zero Dirichlet boundary conditions, are given, where L is a vector valued second order uniformly elliptic differential operator, and f and g are vector valued Carathéodory functions. The method builds on a priori estimates for the Leray-Schauder continuation principle, the general theory of superposition operators in ideal function spaces, and recent results on Orlicz spaces of vector- valued functions.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35J55
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 4127697
zbMATH Keywords: second order quasilinear elliptic systems
zbMATH Keywords: zero Dirichlet boundary conditions
zbMATH Keywords: Leray-Schauder continuation principle
zbMATH Keywords: Orlicz spaces
reviewed by: Jürgen Appell
MaRDI profile type: Publication
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full work available at URL: 0022-247x(90)90428-i
OpenAlex ID: W1998369635
description: scientific article; zbMATH DE number 4127697