Periodic and Antiperiodic Solutions for a Second-Order Hamiltonian System With Nonlinearity Depending on Derivative

Abstract

Some existence results of periodic solution are obtained for a class of second-order Hamiltonian systems with nonlinearity depending on derivative. We prove that there exists T0>0 such that, for any T<T0, the provided Hamiltonian system has a nontrivial T-periodic and T/2-antiperiodic solution via linking theorem and iteration method.