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

This paper is concerned with the following nonperiodic Hamiltonian elliptic system { − Δ u + V ( x ) u = H v ( x , u , v ) x ∈ R N , − Δ v + V ( x ) v = H u ( x , u , v ) x ∈ R N , u ( x ) → 0 , v ( x ) → 0 as | x | → ∞ , where z = ( u , v ) : R N → 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.