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Homoclinic orbits of a Hamiltonian system

  • Y. Ding
  • M. Willem

Abstract.

We establish existence results of homoclinic orbits of the first order time-dependent Hamiltonian system \(\dot z = {\Cal J} H_z (t, z),\) where H(t, z) depends periodically on \(t, H(t, z) = \frac{1}{2} z{\Cal L} (t) z + W (t, z), L(t)\) is a symmetric matrix valued function and W(t, z) satisfies certain global superquadratic condition. We relax partly the assumption often used before: L is independent of t and \(sp({\Cal J} L)\cap i\Bbb{R} = \phi.\)

Key words. Homoclinic orbits, Hamiltonian systems, linking theorem, concentation-compactness. 

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Copyright information

© Birkhäuser Verlag, Basel, 1999

Authors and Affiliations

  • Y. Ding
    • 1
  • M. Willem
    • 2
  1. 1.Inst. of Math., Academia Sinica, 100080 Beijing, P.R. ChinaCN
  2. 2.Dép. Math. U.C.L., 2 ch. du Cyclotron, B1348 Louvain-la-Neuve, BelgiumBE

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