Abstract and Applied Analysis
Volume 2008 (2008), Article ID 756934, 13 pages
doi:10.1155/2008/756934

Bifurcation for second-order Hamiltonian systems with periodic boundary conditions

Abstract

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.