Blow-up and Decay for a Pseudo-parabolic Equation with Nonstandard Growth Conditions

Abstract

This paper deals with a pseudo-parabolic equation involving variable exponents under homogeneous Dirichlet boundary value condition. The authors first develop the potential well method to prove a threshold result on the existence or nonexistence of global solutions to the equation when the initial energy is less than the mountain pass level dd. In the case of high energy initial data, a new characterization for the nonexistence of global solution is also given. These results extend and improve some recent results obtained by Di et al. [9]