Existence results for some nonlinear elliptic equations with measure data in Orlicz-Sobolev spaces

Abstract

We prove the existence results in the setting of Orlicz spaces for the following nonlinear elliptic equation: $$A(u)+g(x,u,Du)=\mu, $$ where A is a Leray-Lions operator defined on $D(A)\subset W_{0}^{1}L_{M}(\Omega)$ , while g is a nonlinear term having a growth condition with respect to Du, but does not satisfy any sign condition. The right-hand side μ is a bounded Radon measure data.