Heteroclinic solutions in singularly perturbed discontinuous differential equations: a non-generic case

Heteroclinic solutions in singularly perturbed discontinuous differential equations: a non-generic case

We derive Melnikov type conditions for the persistence of heteroclinic solutions in perturbed slowly varying discontinuous differential equations. Opposite to [J. Differential Equations 400(2024), 314–375] we assume that the unperturbed (frozen) equation has a parametric system of heteroclinic solut...

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Bibliographic Details
Main Authors: Flaviano Battelli, Michal Fečkan, JinRong Wang
Format: Article
Language:English
Published: University of Szeged 2024-06-01
Series:Electronic Journal of Qualitative Theory of Differential Equations
Subjects:
discontinuous differential equations
heteroclinic solutions
melnikov conditions
persistence
Online Access:http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=10826
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Summary:We derive Melnikov type conditions for the persistence of heteroclinic solutions in perturbed slowly varying discontinuous differential equations. Opposite to [J. Differential Equations 400(2024), 314–375] we assume that the unperturbed (frozen) equation has a parametric system of heteroclinic solutions and extend a result in [SIAM J. Math. Anal. 18(1987), 612–629] and [SIAM J. Math. Anal. 19(1988), 1254–1255] to higher dimensional non-Hamiltonian discontinuous singularly perturbed differential equations.
ISSN:1417-3875

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