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.

Bifurcation for second order Hamiltonian systems with periodic boundary conditions

IANNIZZOTTO, ANTONIO;
2008

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.
Bifurcation theory; Systems of ordinary differential equations; Periodic solutions
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11584/18714
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