Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
844640 | Nonlinear Analysis: Theory, Methods & Applications | 2007 | 22 Pages |
Abstract
This paper treats the occurrence of homoclinic solutions in planar systems with discontinuous right-hand side. More precisely, we deal with a TT-periodic perturbed system such that the unperturbed system is an autonomous possessing homoclinic orbit. By means of the so-called “non-smooth” Melnikov function there is shown the existence of a homoclinic solution for a perturbed system. The non-smooth Melnikov function is derived, and the method of how to find it in concrete problems is also introduced.
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Authors
Peter Kukučka,