Nonlinear singular elliptic problem of Schrödinger type involving p(x)-Laplacian operator

Abstract

This paper investigates the existence of weak solution for a class of nonlinear singular elliptic problem of Schrödinger type involving the $p(x)$-Laplacian operator in a bounded domain in $\mathbb{R}^{N}$. Under certain additional assumptions on the nonlinearities, the corresponding functional satisfies the Palais-Smale condition. Then, by applying the Mountain Pass Theorem, we can demonstrate the existence of weak solution for the problem at hand.