Solutions of a second-order Hamiltonian system with periodic boundary conditions

Pages: 1053 - 1067, Volume 9, Issue 4, July 2010

doi:10.3934/cpaa.2010.9.1053       Abstract        Full Text (175.7K)       Related Articles

Qiong Meng - School of Mathematical Sciences and Computing Technology, Central South University, Changsha, Hunan 410083, China (email)
X. H. Tang - School of Mathematical Sciences and Computing Technology, Central South University, Changsha, Hunan 410083, China (email)

Abstract: By using the least action principle and the minimax methods, some existence theorems are obtained existence of solutions to a second-order Hamiltonian system with periodic boundary conditions in the cases when the gradiant of the nonlinearity is bounded sublinearly and linearly respectively.

Keywords:  Second-order Hamiltonian system, periodic boundary condition, least action principle, saddle point theorem.
Mathematics Subject Classification:  34C25, 58E50, 70H05.

Received: September 2009;      Revised: January 2010;      Published: April 2010.