Note on classification of initial energy to a pseudo-parabolic p -Laplacian equation

This paper deals with a pseudo-parabolic p-Laplacian equation subject to zero Dirichlet boundary conditions. We determine the singularity of solutions in the critical initial energy case, which completes the classification of initial energy and Nehari functional on the existence of global existence and blow-up solutions. Moreover, we extend the ranges of exponents corresponding to the spatial dimensions, which have been studied before in the sub- and super-critical initial energy cases, respectively.