Existence of Solution for a General Class of Strongly Nonlinear Elliptic Problems Having Natural Growth Terms and $L^1$ -Data

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.

Author Details

Youssef Akdim

Morad Ouboufettal