Multiple solutions of perturbed superquadratic second order Hamiltonian systems

Abstract

In this paper we prove the existence of infinitely many distinct Tperiodic solutions for the perturbed second order Hamiltonian system q + V(q) = /(') under the conditions that V:RN -» R is continuously difterentiable and superquadratic, and that / is square integrable and 7-periodic.In the proof we use the minimax method of the calculus of variation combining with a priori estimates on minimax values of the corresponding functionals.Then for any given T, R > 0 and T-periodic function f E L2([0 ,T],RN), the Hamiltonian system (1.1) possesses a T-periodic solution q(t) with max \q(t)\ > R.7€[0,r]' Here q = d q/dt , V is the gradient of V, and we denote by p • q the scalar product in R^ .