New type of solutions for the critical Lane-Emden system

In this paper, we consider the critical Lane-Emden system -Δ u=K_1(y)v^p, y∈ℝ^N, -Δ v=K_2(y)u^q, y∈ℝ^N, u,v>0, where N≥ 5, p,q∈ (1,∞) with 1/p+1+1/q+1=N-2/N, K_1(y) and K_2(y) are positive radial potentials. Under suitable conditions on K_1(y) and K_2(y), we construct a new family of solutions to this system, which are centred at points lying on the top and the bottom circles of a cylinder.