Ground state solution for a class of Choquard equation with indefinite periodic potential

Abstract

This paper is concerned with a class of nonlinear Choquard equation with potential. We assume the potential satisfies general indefinite periodic condition, so the Schrödinger operator has purely continuous spectrum and the associate energy functional is strongly indefinite. Applying the generalized Nehari manifold method developed by Szulkin and Weth, we prove the existence of ground state solution.