Asymptotically linear elliptic systems in

In this paper, we show that semilinear elliptic systems of the form { − ( Δ u − u ) − μ ( Δ v − v ) = g ( v ) , − ( Δ v − v ) − λ ( Δ u − u ) = f ( u ) , x ∈ R N possess at least one nontrivial solution pair ( u , v ) ∈ H 1 ( R N ) × H 1 ( R N ) , where λ and μ are positive numbers, f ( t ) and g ( t ) are continuous functions on R and asymptotically linear as t → + ∞ .