This paper deals with the following critical elliptic systems of Hamiltonian type, which are variants of the critical Lane-Emden systems and analogous to the prescribed curvature problem: {−Δu1=K1(y)u2p,y∈RN,−Δu2=K2(y)u1q,y∈RN,u1,u2>0, where N≥5,p,q∈(1,∞) with [Formula presented], K1(y) and K2(y) are positive radial potentials. At first, under suitable conditions on K1,K2 and the certain range of the exponents p,q, we construct an unbounded sequence of non-radial positive vector solutions, whose energy can be made arbitrarily large....
