Existence and nonexistence of ground states for asymptotically periodic double phase problems

In this paper we consider a class of double phase problems with asymptotically periodic reaction. We study the existence and nonexistence of ground states, and meanwhile discuss whether the nonlinearity is (q−1)-superlinear or asymptotically (q−1)-linear at infinity. The proof is based on the method of Nehari manifold and concentration compactness principle.