Exponential dichotomies, the Fredholm Alternative, and transverse homoclinic orbits in partial functional differential equations

Shigui Ruan, Weinian Zhang

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

In this paper we investigate the transversality of homoclinic orbits in partial functional differential equations. We first discuss the exponential dichotomies for linear operator equations. Then we show that the Fredholm Alternative holds if the homogeneous equation has exponential dichotomies on R. Transversality of homoclinic orbits for periodically perturbed partial functional differential equations is studied using the Liapunov-Schmidt method and the Melnikov integral.

Original languageEnglish (US)
Pages (from-to)759-777
Number of pages19
JournalJournal of Dynamics and Differential Equations
Volume17
Issue number4
DOIs
StatePublished - Oct 2005

Keywords

  • Exponential dichotomy
  • Liapunov-Schmidt method
  • Melnikov integral
  • Partial functional differential equations
  • The Fredholm Alternative
  • Transverse homoclinic orbit

ASJC Scopus subject areas

  • Analysis

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