Ground states for fractional linear coupled systems via profile decomposition *

Abstract

Abstract In this work we study existence and nonexistence of weak and ground state (least energy) solutions for a class of nonlocal linearly coupled elliptic systems. We deal with nonautonomous nonlinearities that may not satisfy any kind of monotonicity, also the related potentials may not have any kind of smoothness. In order to obtain ground states, instead of applying the well known methods of Nehari–Pohozaev manifold, we introduce new arguments and techniques whose are based on a Pohozaev type identity, a concentration-compactness principle and a profile decomposition type result.