Asymptotically linear Schrödinger equations with sign-changing potential

Abstract

Abstract In this paper, we show that the following system: (0.1) − Δ u + V ( x ) u = g ( x , v ) , − Δ v + V ( x ) v = f ( x , u ) , x ∈ R N possesses at least one non-trivial solution pair ( u , v ) , where f ( x , t ) , g ( x , t ) are continuous functions on R N × R and asymptotically linear as t → + ∞ , and V ( x ) is allowed to be sign-changing.