Existence and multiplicity of solutions for asymptotically linear nonperiodic Hamiltonian elliptic system

This paper is concerned with the following nonperiodic Hamiltonian elliptic system {−Δu+V(x)u=Hv(x,u,v)−Δv+V(x)v=Hu(x,u,v)x∈RN,u(x),v(x)→0as|x|→∞, where z=(u,v):RN→R×Rz=(u,v):RN→R×R, N≥3N≥3. Assuming the potential VV is nonperiodic and sign-changing, H(x,z)H(x,z) is nonperiodic in xx and asymptotically quadratic in z=(u,v)z=(u,v), existence and multiplicity of solutions are obtained via a variational approach.