Periodic solutions for a class of first order super-quadratic Hamiltonian system

Based on a developed local linking theorem, by replacing the Palais–Smale condition with a Cerami one, we consider the following unbounded Hamiltonian system: ∂tu− xu +V (x)u = Hv(t, x,u, v), −∂t v − xv + V (x)v = Hu(t, x,u, v) for (t, x) ∈ R×Ω, (H) where Ω ⊂ RN, N 1, is a bounded domain with smooth boundary ∂Ω. The nonlinearities are assumed to be super-quadratic at the infinite, which are different from those investigated previously. © 2006 Elsevier Inc. All rights reserved.