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

This paper investigates the existence of weak solution for a class of nonlinear singular elliptic problem of Schr?dinger type involving the p(x)-Laplacian operator in a bounded domain in RN. 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 considered problem.