Potential well method for p(x)-Laplacian equations with variable exponent sources. (December 2020) - Nhan, Le Cong; Chuong, Quach Van; Truong, Le Xuan
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.