Existence of solution for a general class of strongly nonlinear elliptic problems without sign condition

Document Type : Original Article

Authors

Morad Ouboufettal

Youssef Akdim

L2MASI Laboratory, Department of Mathematics, Faculty of Sciences Dhar El Mahraz, University Sidi Mohamed Ben Abdellah, P.O. Box 1796, Atlas Fez, Morocco

10.22034/kjm.2025.450905.3177

Abstract

In this paper, we study existence and $L^\infty-$regularity results for a general class of strongly nonlinear elliptic problems associated with the differential inclusion $$\beta(u)+A(u)+H(x,u,Du)\ni f$$ where $A$ is a Leray-Lions operator from $W^{1,p}_0(\Omega)$ into its dual, $\beta$ is a maximal monotone mapping such that $0 \in \beta(0) $, while $H(x,s,\xi)$ is a nonlinear term which satisfies some growth condition but no sign-condition on $s$. The right hand side $ f$ is assumed to belong to $L^{\infty}(\Omega)$.

Keywords

$L^\infty-$estimate

Leray-Lions operator

maximal monotone graph

Sobolev spaces

weak solution

Subjects

• 35 Partial differential equations

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