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Bifurcation for second-order Hamiltonian systems with periodic boundary conditions. (English) Zbl 1144.37025
Summary: 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.
MSC:
37J45Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
37J20Bifurcation problems (finite-dimensional Hamiltonian etc. systems)
47J30Variational methods (nonlinear operator equations)
37C60Nonautonomous smooth dynamical systems
34C25Periodic solutions of ODE