Bifurcation for Second-Order Hamiltonian Systems with Periodic Boundary Conditions. (2nd January 2008)

• Record Type: Journal Article
• Authors: Faraci, Francesca; Iannizzotto, Antonio
• Other Names: Mawhin Jean Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2008(2008)
• Publication Date: 2008-01-02
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2008/756934
• Languages: English
• ISSNs: 1085-3375

Abstract

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.