Existence Results for Periodic Boundary Value Problems in Second-Order Hamiltonian Systems
Tingting Hu *
College of Artificial Intelligence and Information Technology, Nanjing University of Chinese Medicine, Nanjing 210023, P.R. China.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Second order Hamiltonian system, periodic potential, solutions, critical point, operator equation