Periodic Solutions in Slowly Varying Discontinuous Differential Equations: The Generic Case

Flaviano Battelli and Michal Fečkan
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Flaviano Battelli: Department of Industrial Engineering and Mathematics, Marche Polytecnic University, 60121 Ancona, Italy
Michal Fečkan: Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská Dolina, 84248 Bratislava, Slovakia

Mathematics, 2021, vol. 9, issue 19, 1-21

Abstract: We study persistence of periodic solutions of perturbed slowly varying discontinuous differential equations assuming that the unperturbed (frozen) equation has a non singular periodic solution. The results of this paper are motivated by a result of Holmes and Wiggins where the authors considered a two dimensional Hamiltonian family of smooth systems depending on a scalar variable which is the solution of a singularly perturbed equation.

Keywords: discontinuous differential equations; periodic solutions; persistence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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