Subharmonic Solutions in Singular Systems

✍ Scribed by Flaviano Battelli; Michal Fečkan

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 915 KB
• Volume: 132
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.1996.0169

✦ Synopsis

We consider the problem of bifurcation from homoclinic towards periodic orbits for a periodic singular system of differential equations. We use a functional analytic approach and the Lyapunov Schmidt method to obtain a bifurcation function for this problem which tends, as = Ä 0 + , to the well-known Melnikov function for the bifurcation towards transverse homoclinic orbits. We also study the behavior of the bifurcation functions as the period of the periodic orbit tends to infinity.