New asymptotically quadratic conditions for Hamiltonian elliptic systems

This paper is concerned with the following Hamiltonian elliptic system {-Delta u + V(x)u = Wv(x, u, v), x is an element of R-N, -Delta v + V(x) v = Wu(x, u, v), x is an element of R-N, where z = (u, v) : R-N -> R-2, V(x) and W(x, z) are 1-periodic in x. By making use of variational approach for strongly indefinite problems, we obtain a new existence result of nontrivial solution under new conditions that the nonlinearity W(x, z) := 1/2 V-infinity(x)vertical bar Az vertical bar(2) + F(x, z) is general asymptotically quadratic, where V-infinity(x) is an element of (R-N, R) is 1-periodic in x and inf(RN) V-infinity(x) > min (RN) V(x), and A is a symmetric non-negative definite matrix.