Existence of Positive Ground State Solutions for Choquard Systems

Abstract We study the existence of positive ground state solution for Choquard systems. In the autonomous case, we prove the existence of at least one positive ground state solution by the Pohozaev manifold method and symmetric-decreasing rearrangement arguments. Moreover, we show that each positive ground state solution is radial symmetric. While, in the nonautonomous case, a positive ground state solution is obtained by using a monotonicity trick and a global compactness lemma. We remark that, under our assumptions of the nonlinearity W u {W_{u}} , the search of ground state solutions cannot be reduced to the study of critical points of a functional restricted to a Nehari manifold.