Existence of Solution for a General Class of Strongly Nonlinear Elliptic Problems Having Natural Growth Terms and $L^1$ -Data
Year: 2023
Author: Youssef Akdim, Morad Ouboufettal
Analysis in Theory and Applications, Vol. 39 (2023), Iss. 1 : pp. 53–68
Abstract
This paper is concerned with the existence of solution for a general class of strongly nonlinear elliptic problems associated with the differential inclusion $$β(u)+A(u)+g(x,u,Du) \ni f,$$ where $A$ is a Leray-Lions operator from $W^{1,p}_0(Ω)$ into its dual, $β$ maximal monotone mapping such that $0 ∈ β(0),$ while $g(x,s, ξ)$ is a nonlinear term which has a growth condition with respect to $ξ$ and no growth with respect to $s$ but it satisfies a sign-condition on $s.$ The right hand side $f$ is assumed to belong to $L^1(Ω).$
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-2020-0049
Analysis in Theory and Applications, Vol. 39 (2023), Iss. 1 : pp. 53–68
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Sobolev spaces Leray-Lions operator trunctions maximal monotone graphe.