A strongly nonlinear elliptic equation having natural growth terms and \(L^1\) data
type: Item
instance of: scholarly article
title: A strongly nonlinear elliptic equation having natural growth terms and \(L^1\) data
zbMATH Open document ID: 0942.35079
DOI: 10.1016/S0362-546X(98)00180-1
author: A. Elmahi
author: A. Benkirane
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2000-07-12T00:00:00Z
review text: This paper deals with the Dirichlet problem for the equation \[ A(u)+g(x,u,\nabla u)=f \] in the setting of the Orlicz-Sobolev space \(W^1L_M(\Omega)\), where \(\Omega\) is a bounded open subset of \(\mathbb R^N\), \(A(u)=-\text{div}(a(x,u,\nabla u))\), \(f\in L^1(\Omega)\). Under the assumption that the \(N\)-function \(M\) satisfies the \(\Delta_2\) condition and under corresponding growth, coerciveness and monotonicity conditions on the functions \(a\) and \(g\) the authors prove the existence of a solution of the problem under consideration.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 1389518
zbMATH Keywords: Orlicz-Sobolev spaces
zbMATH Keywords: truncations
zbMATH Keywords: strongly nonlinear elliptic problem
reviewed by: Alexander A. Kovalevsky
MaRDI profile type: Publication
full work available at URL: s0362-546x(98)00180-1
OpenAlex ID: W2001370571
description: scientific article; zbMATH DE number 1389518