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Volume 39, Issue 1
Existence of Solution for a General Class of Strongly Nonlinear Elliptic Problems Having Natural Growth Terms and $L^1$ -Data

Youssef Akdim & Morad Ouboufettal

Anal. Theory Appl., 39 (2023), pp. 53-68.

Published online: 2023-03

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  • 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 $L^1(Ω).$

  • AMS Subject Headings

35J15, 35J20, 35J60

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COPYRIGHT: © Global Science Press

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@Article{ATA-39-53, author = {Akdim , Youssef and Ouboufettal , Morad}, title = {Existence of Solution for a General Class of Strongly Nonlinear Elliptic Problems Having Natural Growth Terms and $L^1$ -Data}, journal = {Analysis in Theory and Applications}, year = {2023}, volume = {39}, number = {1}, pages = {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 $L^1(Ω).$

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2020-0049}, url = {http://global-sci.org/intro/article_detail/ata/21461.html} }
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 -

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 $L^1(Ω).$

Akdim , Youssef and Ouboufettal , Morad. (2023). Existence of Solution for a General Class of Strongly Nonlinear Elliptic Problems Having Natural Growth Terms and $L^1$ -Data. Analysis in Theory and Applications. 39 (1). 53-68. doi:10.4208/ata.OA-2020-0049
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