Potential well method for [formula omitted]-Laplacian equations with variable exponent sources

Abstract

In this paper, we study a class of semilinear p(x)-Laplacian equations with variable exponent sources. By using potential well method, we first prove a threshold results on the existence and nonexistence of global solutions to the equations when initial energy is less than the mountain pass level d. In the former case we also show the decay properties of energy functional. We finally obtain the non-global existence results with high energy initial data.