Homoclinic orbits in a first order superquadratic hamiltonian system: Convergence of subharmonic orbits

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Abstract

We consider the existence of homoclinic orbits for a first order Hamiltonian system z ̇ = JHz(t, z). We assume H(t, z) is of form H(t, z) = 1 2(Az, z) + W(t, z), where A is a symmetric matrix with δ(JA)∩iR = ∅ and W(t, z) is 2π-periodic in t and has superquadratic growth in z. We prove the existence of a nontrivial homoclinic solution z(t) and subharmonic solutions (zT(t))Tε{lunate}N (i.e., 2πT-periodic solutions) of (HS) such that ZT(t) → Z(t) in Cloc1(R,R2N) as T → ∞.

Original languageEnglish
Pages (from-to)315-339
Number of pages25
JournalJournal of Differential Equations
Volume94
Issue number2
DOIs
Publication statusPublished - 1991 Dec
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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