Ground states for a linearly coupled indefinite Schrödinger system with steep potential well

Abstract

In this paper, we study a class of linearly coupled Schrödinger systems with steep potential wells, which arises from Bose–Einstein condensates. The existence of positive ground states is investigated by exploiting the relation between the Nehari manifold and fiberring maps. Some interesting phenomena are that we do not need the weight functions in the nonlinear terms to be integrable or bounded and we can relax the upper control condition of the coupling function. Moreover, the decay rate and concentration phenomenon of positive ground states are also studied.