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

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 T 0 > 0 such that, for any T < T 0 , the provided Hamiltonian system has a nontrivial T ‐periodic and T /2‐antiperiodic solution via linking theorem and iteration method.