TY - JOUR
T1 - Existence of Solution for a General Class of Strongly Nonlinear Elliptic Problems Having Natural Growth Terms and $L^1$ -Data
AU - Akdim , Youssef
AU - Ouboufettal , Morad
JO - Analysis in Theory and Applications
VL - 1
SP - 53
EP - 68
PY - 2023
DA - 2023/03
SN - 39
DO - http://doi.org/10.4208/ata.OA-2020-0049
UR - https://global-sci.org/intro/article_detail/ata/21461.html
KW - Sobolev spaces, Leray-Lions operator, trunctions, maximal monotone graphe.
AB - <p style="text-align: justify;">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 $L^1(Ω).$</p>