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 language | English (US) |
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Pages (from-to) | 759-777 |
Number of pages | 19 |
Journal | Journal of Dynamics and Differential Equations |
Volume | 17 |
Issue number | 4 |
DOIs | |
State | Published - 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