Existence and uniqueness of weak solution of p(X)-laplacian in sobolev spaces with variable exponents in complete manifolds

Abstract

The paper deals with the existence and uniqueness of a non-trivial solution to non-homogeneous p(x)−laplacian equations, managed by non polynomial growth operator in the framework of variable exponent Sobolev spaces on Riemannian manifolds. The mountain pass Theorem is used.