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Lithuanian Mathematical Journal

, Volume 58, Issue 2, pp 185–197 | Cite as

Distributional van der Pol equation with state-dependent impulses

  • Irena Rachůnková
  • Jan Tomeček
Article
  • 46 Downloads

Abstract

We investigate the distributional differential van der Pol equation with impulsive forcing term. We prove the existence of a periodic solution without global or local Lipschitz conditions for impulsive functions and find a simple assumption on the parameter of the van der Pol equation guaranteeing its solvability.

Keywords

distributional van der Pol equation state-dependent impulses existence periodic solution impulsive model 

MSC

34A37 34C25 

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematical Analysis and Applications of Mathematics, Faculty of SciencePalacký UniversityOlomoucCzechia

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