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

Author

Listed:
  • 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
    Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 81473 Bratislava, Slovakia)

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.

Suggested Citation

  • Flaviano Battelli & Michal Fečkan, 2021. "Periodic Solutions in Slowly Varying Discontinuous Differential Equations: The Generic Case," Mathematics, MDPI, vol. 9(19), pages 1-21, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2449-:d:648793
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