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 $\sigma$-compact. Then, we deal with a linear system depending on a real parameter $\lambda >0$ and on a function $u$, and prove that there exists ${\lambda }^{\ast }$ such that the set of the functions $u$, such that the system admits nontrivial solutions, contains an accumulation point.