Existence and multiplicity of nontrivial solutions for nonlinear fractional differential systems with <i>p</i>‐Laplacian via critical point theory

Abstract

In this paper, the existence and multiplicity of nontrivial solutions are obtained for nonlinear fractional differential systems with p ‐Laplacian by combining the properties of fractional calculus with critical point theory. Firstly, we present a result that a class of p ‐Laplacian fractional differential systems exists infinitely many solutions under the famous Ambrosetti‐Rabinowitz condition. Then, a criterion is given to guarantee that the fractional systems exist at least 1 nontrivial solution without satisfying Ambrosetti‐Rabinowitz condition. Our results generalize some existing results in the literature.