Existence of entropy solution to the Neumann problem for elliptic equation with measure-valued potential

In a bounded or unbounded domain in $\mathbb{R}^n$, the Neumann problem for a non-linear second order elliptic equation with measure-valued potential is considered. The assumptions on the structure of the equation are stated in terms of a generalized $N$-function. The existence of an entropy solution to the problem is proved.