Existence and non-degeneracy of positive multi-bubbling solutions to critical elliptic systems of Hamiltonian type

This paper deals with the following critical elliptic systems of Hamiltonian type, which are variants Lane-Emden and analogous to prescribed curvature problem:{−Δu1=K1(y)u2p,y∈RN,−Δu2=K2(y)u1q,y∈RN,u1,u2>0, where N≥5,p,q∈(1,∞) 1p+1+1q+1=N−2N, K1(y) K2(y) positive radial potentials. At first, under suitable conditions on K1,K2 certain range exponents p,q, we construct an unbounded sequence non-radial vector solutions, whose energy can be made arbitrarily large. Moreover, prove a type non-degeneracy result by use various Pohozaev identities, is great interest independently. The indefinite linear operator strongly coupled nonlinearities make Hamiltonian-type in stark contrast both Gradient single equations study problems. It worth noting that, higher-dimensional cases (N≥5), there have been no results existence infinitely many bubbling solutions systems, either or type.