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A Survey on the Melnikov Theory for Implicit Ordinary Differential Equations with Applications to RLC Circuits

  • Michal FečkanEmail author
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 200)

Abstract

Our recent results are presented on the development of the Melnikov theory in investigation of implicit ordinary differential equations with small amplitude perturbations. In particular, the persistence of orbits connecting singularities in finite time is studied provided that certain Melnikov like conditions hold. Achievements on reversible implicit ordinary differential equations are also considered. Applications are given to nonlinear systems of RLC circuits.

Keywords

Implicit ordinary differential equations Impasse points IK-singularities RLC circuits 

2010 MSC

34A09 37C60 47N70 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and InformaticsComenius University in BratislavaBratislavaSlovakia
  2. 2.Mathematical Institute, Slovak Academy of SciencesBratislavaSlovakia

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