Existence of Weak Solutions for Nonlinear Time-Fractional p-Laplace Problems

Abstract

The existence of weak solution for $p$-Laplace problem is studied in the paper. By exploiting the relationship between the Nehari manifold and fibering maps and combining the compact imbedding theorem and the behavior of Palais-Smale sequences in the Nehari manifold, the existence of weak solutions is established. By means of the Arzela-Ascoli fixed point theorem, some existence results of the corresponding time-fractional equations of the $p$-Laplace problem are obtained.