Existence of solutions for a class of second-order Hamiltonian systems with impulsive effects

In this paper, a class of second-order Hamiltonian systems with impulsive effects are considered. We establish some sufficient conditions for the existence of solutions for the second-order Hamiltonian systems with impulsive effects {ü(t)=∇F(t,u(t)),a.e. t∈[0,T];u(0)−u(T)=u̇(0)−u̇(T)=0,Δu̇i(tj)=u̇i(tj+)−u̇i(tj−)=Iij(ui(tj)),i=1,2,…,N,j=1,2,…,p, where t0=0