Existence of periodic solutions of a particular type of super-quadratic Hamiltonian systems

This paper considers the Hamiltonian systems with new super-quadratic conditions covering the case Hˆ(t,z)=(|p|1+μν+|q|1+νμ)(ln⁡(1+|z|ξˆ))ηˆ, where ξˆ,ηˆ,μ,ν>1 with 1μ+1ν<1 and μ2ν<νμ<μν<1+νμ. Using the mini-max principle, we obtain the existence of the periodic solutions.