Homoclinic Solutions of Differential Equations

  • Maria do Rosário Grossinho
  • Stepan Agop Tersian
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 52)

Abstract

In recent years, starting with works of Bolotin [Bol], Coti-Zelati, Ekeland and Séré [CZES], Coti-Zelati & Rabinowitz [CZR1], [CZR2], Rabinowitz [Ra4], variational methods have been applied to study the existence of homoclinic and heteroclinic solutions of second-order equations and Hamiltonian systems. The search for homoclinic and heteroclinic solutions is a classical problem, originated from the work of Poincaré and has been developed from several points of view. Existence of homoclinic solutions can be obtained by analyzing the intersection properties of the stable and unstable manifolds of the fixed points. There is a standard method to find infinitely nearby homoclinics provided that the stable and unstable manifolds of a fixed point intersect transversally. For this approach we refer the reader to Moser [Mo], Guckenheimer & Holmes [GH], Wiggins [Wig].

Keywords

Hamiltonian System Vortex Ring Nontrivial Solution Unstable Manifold Homoclinic Orbit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Maria do Rosário Grossinho
    • 1
    • 2
  • Stepan Agop Tersian
    • 3
  1. 1.ISEGUniversidade Técnica de LisboaPortugal
  2. 2.CMAFUniversidade de LisboaPortugal
  3. 3.University of RousseBulgaria

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