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:equation(0.1){∂tu−Δxu+V(x)u=Hv(t,x,u,v),−∂tv−Δxv+V(x)v=Hu(t,x,u,v)for (t,x)∈R×Ω, where Ω⊂RNΩ⊂RN, N⩾1N⩾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.