Ground state solutions of a fractional advection–dispersion equation

Abstract

In this paper, a class of fractional Sturm–Liouville advection–dispersion equations with instantaneous and noninstantaneous impulsive boundary conditions is considered. At the beginning, the existence of at least one nontrivial ground state solution is proved by the method of Nehari manifold without the Ambrosetti–Rabinowitz condition. Then, the existence of infinitely many nontrivial weak solutions is obtained by using the genus properties. Finally, an example is given to illustrate the main results obtained in this paper.