Existence and non-existence of global solutions of pseudo-parabolic equations involving p(x)-Laplacian and logarithmic nonlinearity

Abstract

In this paper, we consider a class of pseudo-parabolic equations involving p(x)-Laplacian and logarithmic nonlinearity. By using the potential well method, we give some threshold results on existence or nonexistence of global weak solutions when the initial energy is subcritical. Moreover, the decay estimates for the global bounded solutions and the growth estimates for the global unbounded solutions are also concerned.