Abstract and Applied Analysis
Volume 2008 (2008), Article ID 756934, 13 pages
Research Article

Bifurcation for Second-Order Hamiltonian Systems with Periodic Boundary Conditions

Francesca Faraci and Antonio Iannizzotto

Dipartimento di Matematica e Informatica, Università di Catania, Viale A. Doria 6, Catania 95125, Italy

Received 12 March 2007; Revised 21 June 2007; Accepted 18 December 2007

Academic Editor: Jean Mawhin

Copyright © 2008 Francesca Faraci and Antonio Iannizzotto. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Through variational methods, we study nonautonomous systems of second-order ordinary differential equations with periodic boundary conditions. First, we deal with a nonlinear system, depending on a function u, and prove that the set of bifurcation points for the solutions of the system is not σ-compact. Then, we deal with a linear system depending on a real parameter λ>0 and on a function u, and prove that there exists λ such that the set of the functions u, such that the system admits nontrivial solutions, contains an accumulation point.