Singular solutions in a pseudo-parabolic p-Laplacian equation involving singular potential

This paper deals with a pseudo-parabolic p-Laplacian equation involving singular potential. Firstly, we determine the existence and uniqueness of weak solution in the Sobolev spaces by using Galerkin methods and some priori estimates. Secondly, in the frame of variational methods, we classify the blow-up and the global existence of weak solutions by covering all kinds of initial energy. Moreover, we obtain the upper bounds of blow-up time for all cases. The results of this paper extend the ones in Lian et al. J Differ Equ 269:4914–4959, 2020.