Infinitely many solutions for superlinear periodic Hamiltonian elliptic systems

This paper is concerned with the following periodic Hamiltonian elliptic system: -Delta u + V(x)u = H-v(x, u, v), x is an element of R-N, -Delta v + V(x)v = H-u(x, u, v), x is an element of R-N, u(x) -> 0, v(x) -> 0 as vertical bar x vertical bar -> infinity. Assuming the potential V is periodic and 0 lies in a gap of sigma(-Delta + V), H(x, z) is periodic in x and superquadratic in z = (u, v). We establish the existence of infinitely many large energy solutions by the generalized variant fountain theorem developed recently by Batkam and Colin.