#### Badr El Haji, Mostafa El Moumni, Entropy solutions of nonlinear elliptic equations with $L^1$-data and without strict monotonocity conditions in weighted Orlicz-Sobolev spaces, Vol. 2021 (2021), Article ID 8, pp. 1-17

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DOI: 10.23952/jnfa.2021.8

Received October 17, 2020; Accepted March 4, 2021; Published March 22, 2021

Abstract. In this paper, we study the existence of entropy solutions for a class of nonlinear elliptic problems in weighted Orlicz-Sobolev spaces of with the form $A u+g(x, u)=f$, where $A(u)=-\mbox{div }(\rho(x)a(x,u,\nabla u))$ is a Leray-Lions operator defined from the weighted Orlicz-sobolev spaces $W_{0}^{1}L_{M}(\rho,\Omega)$ into its dual. The right hand side $f \in L^{1}(\Omega),$ and the function $a(x, s, \xi)$ satisfies only the large monotonicity instead of the monotonicity strict.

Badr El Haji, Mostafa El Moumni, Entropy solutions of nonlinear elliptic equations with $L^1$-data and without strict monotonocity conditions in weighted Orlicz-Sobolev spaces, Journal of Nonlinear Functional Analysis, Vol. 2021 (2021), Article ID 8, pp. 1-17