Variational nonlinear elliptic equations having large monotonocity in Musielak-Sobolev spaces

We study in Musielak-Sobolev space, the existence of entropy solution for a class of nonlinear elliptic problems, in the case the Leray-Lions operator satisfies only the large monotonicity condition and right hand side \(f\in W^{-1} L_{\psi }(\Omega )\) $f\in W^{-1}{L}_{\psi }(\mathrm{\Omega })$ .