Asymptotically linear elliptic systems in RNRN

In this paper, we show that semilinear elliptic systems of the form{−(Δu−u)−μ(Δv−v)=g(v),−(Δv−v)−λ(Δu−u)=f(u),x∈RN possess at least one nontrivial solution pair (u,v)∈H1(RN)×H1(RN)(u,v)∈H1(RN)×H1(RN), where λ and μ   are positive numbers, f(t)f(t) and g(t)g(t) are continuous functions on RR and asymptotically linear as t→+∞t→+∞.