Critical Point Theory For Second Order Hamiltonian Systems

The periodic solutions of Hamiltonian systems are studied by variational methods in this paper.Firstly, the evolution and development of principle of the calculus of variations is introduced, and its applications to Hamiltonian systems; then, some solvability conditions and the corresponding existence results are summed up for periodic solutions of the second order Hamiltonian systems obtained by the least action principle and the minimax methods in variational methods; finally, the existence of periodic solutions for the second order Hamiltonian systemsare proved in "subquadratic" potential condition by using the saddle point theorem in critical point theory.Where A is a real symmetric n×n matrix, T > 0, F ∈C~1(R×R~n,R)and it satisfies...