Bifurcation for Second-Order Hamiltonian Systems with Periodic Boundary Conditions. (2nd January 2008) - Faraci, Francesca; Iannizzotto, Antonio
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 functionu, and prove that the set of bifurcation points for the solutions of the system is notσ -compact. Then, we deal with a linear system depending on a real parameterλ > 0 and on a functionu, and prove that there existsλ ∗ such that the set of the functionsu, such that the system admits nontrivial solutions, contains an accumulation point.