Multiple solutions for asymptotically quadratic and superquadratic elliptic system of Hamiltonian type

This paper is concerned with the following nonperiodic Hamiltonian elliptic system {−Δu+V(x)u=Hv(x,u,v)x∈RN,−Δv+V(x)v=Hu(x,u,v)x∈RN,u(x)→0,v(x)→0as|x|→∞,where z=(u,v):RN→R×R,z=(u,v):RN→R×R,N ≥ 3, and the potential V(x) is nonperiodic and sign-changing. By applying a generalized linking theorem for strongly indefinite functionals, we establish the existence of multiple solutions for asymptotically quadratic nonlinearity as well as the existence of infinitely many solutions for superquadratic nonlinearity.