Bifurcation for second order Hamiltonian systems with periodic boundary conditions

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.