Asymptotically linear Schrödinger equations with sign-changing potential

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