Melnikov method for discontinuous planar systems |
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Authors: | Peter Kukučka |
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Institution: | Karpatská 3, 915 01 Nové Mesto nad Váhom, Slovakia |
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Abstract: | This paper treats the occurrence of homoclinic solutions in planar systems with discontinuous right-hand side. More precisely, we deal with a T-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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Keywords: | 34C37 34A36 34A26 |
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