Existence Results for Periodic Boundary Value Problems in Second-Order Hamiltonian Systems

This paper is dedicated to investigating the existence of solutions for second order Hamiltonian systems with periodic potentials. We generalized some results to the operator equation Ax−∇Φ(x) = 0 by virtue of the critical point theory and the index theory of operator equations. And then we discuss the Sturm-Liouville boundary value problem and the generalized periodic boundary value problem with periodic potential, the existence of solutions is obtained.