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Mathematical Problems in Engineering
Volume 2006, Article ID 85349, 13 pages
http://dx.doi.org/10.1155/MPE/2006/85349

Bifurcations of planar sliding homoclinics

Jan Awrejcewicz,1 Michal Feckan,2 and Pawel Olejnik1

1Department of Automatics and Biomechanics, Technical University of Lodz, 1/15 Stefanowski Street, Lodz 90-924, Poland
2Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Mlynská dolina, Bratislava 842 48, Slovakia

Received 31 August 2005; Accepted 11 September 2005

Copyright © 2006 Jan Awrejcewicz et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study bifurcations from sliding homoclinic solutions to bounded solutions on ℝ for certain discontinuous planar systems under periodic perturbations. Sufficient conditions are derived for such perturbation problems.