Periodic solutions for second-order discrete Hamiltonian systems

Abstract

By using the least action principle and the minimax methods, some existence theorems are obtained for periodic solutions of second-order discrete Hamiltonian systems:

in the cases where the nonlinearity is growing sublinearly or linearly.

Keywords:

• second-order discrete Hamiltonian systems
• periodic solution
• critical point
• sublinear growth or linear growth
• the least action principle
• the saddle point theorem

2000 Mathematics Subject Classification::

• 39A11
• 58E50
• 70H05

Acknowledgement

This project is partially supported by the NNSF (No. 10771215) of China and supported by the Graduate degree thesis Innovation Foundation of Central South University (No: 3960-71131100014) and supported by the Outstanding Doctor degree thesis Implantation Foundation of Central South University (No: 2008yb032).