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Bifurcation for Second‐Order Hamiltonian Systems with Periodic Boundary Conditions

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  • Francesca Faraci
  • Antonio Iannizzotto

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.

Suggested Citation

  • Francesca Faraci & Antonio Iannizzotto, 2008. "Bifurcation for Second‐Order Hamiltonian Systems with Periodic Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2008(1).
    • Handle: RePEc:wly:jnlaaa:v:2008:y:2008:i:1:n:756934
    DOI: 10.1155/2008/756934
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    References listed on IDEAS

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    1. Vladimír Ďurikovič & Monika Ďurikovičová, 2004. "On the solutions of nonlinear initial-boundary value problems," Abstract and Applied Analysis, Hindawi, vol. 2004, pages 1-18, January.
    2. Vladimír Ďurikovič & Monika Ďurikovičová, 2004. "On the solutions of nonlinear initial‐boundary value problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2004(5), pages 407-424.
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