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

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Mathematics Applied to Engineering, Modelling, and Social Issues

Part of the book series: Studies in Systems, Decision and Control ((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.

This work was supported by the Slovak Research and Development Agency (grant number APVV- 14-0378) and the Slovak Grant Agency VEGA (grant numbers 2/0153/16 and 1/0078/17).

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Authors and Affiliations

  1. Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská dolina, 842 48, Bratislava, Slovakia

    Michal Fečkan

  2. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Michal Fečkan

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  1. Michal Fečkan
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Correspondence to Michal Fečkan .

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Editors and Affiliations

  1. Department of Mathematics, University College London, London, UK

    Frank T. Smith

  2. Department of Mathematics, Gauhati University, Guwahati, Assam, India

    Hemen Dutta

  3. Department of Mathematics, Center for Mathematics of Uncertainty, Creighton University, Omaha, NE, USA

    John N. Mordeson

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Fečkan, M. (2019). A Survey on the Melnikov Theory for Implicit Ordinary Differential Equations with Applications to RLC Circuits. In: Smith, F.T., Dutta, H., Mordeson, J.N. (eds) Mathematics Applied to Engineering, Modelling, and Social Issues. Studies in Systems, Decision and Control, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-030-12232-4_4

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  • DOI: https://doi.org/10.1007/978-3-030-12232-4_4

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  • Print ISBN: 978-3-030-12231-7

  • Online ISBN: 978-3-030-12232-4

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