Ground state solutions of Schrödinger system with fractional p-Laplacian

Abstract This article deals with a class of nonlinear fractional p -Laplacian Schr o ̈ $\ddot{o}$ dinger coupled system with critical and subcritical nonlinear terms. Firstly, the existence of a nonnegative ground state solution of the system is proved by the Nehari manifold method and the Ekeland’s variational principle. In addition, through the Ljusternik–Schnirelmann theory, we link the number of solutions to the topology of the set in which the potentials in the system reach their minimum values.