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

Abstract Based on a developed local linking theorem, by replacing the Palais–Smale condition with a Cerami one, we consider the following unbounded Hamiltonian system: (0.1) { ∂ t u − Δ x u + V ( x ) u = H v ( t , x , u , v ) , − ∂ t v − Δ x v + V ( x ) v = H u ( t , x , u , v ) for  ( t , x ) ∈ R × Ω , where Ω ⊂ R N , 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.

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