Existence of positive ground state solutions for the coupled Choquard system with potential

Abstract

AbstractIn this paper, we study the following coupled Choquard system in : where and , in which denotes if and if . The function is a Riesz potential. By using Nehari manifold method, we obtain the existence of a positive ground state solution in the case of bounded potential and periodic potential, respectively. In particular, the nonlinear term includes the well‐studied case and , and the less‐studied case and . Moreover, it seems to be the first existence result for the case .