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A Note on Transformations of Independent Variable in Second Order Dynamic Equations

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Difference Equations and Discrete Dynamical Systems with Applications (ICDEA 2018)

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Abstract

The main purpose of this paper is to show how a transformation of independent variable in dynamic equations combined with suitable statements on a general time scale can yield new results or new proofs to known results. It seems that this approach has not been extensively used in the literature devoted to dynamic equations. We present, in particular, two types of applications. In the first one, an original dynamic equation is transformed into a simpler equation. In the second one, a dynamic equation in a somehow critical setting is transformed into a noncritical case. These ideas will be demonstrated on problems from oscillation theory and asymptotic theory of second order linear and nonlinear dynamic equations.

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Acknowledgements

The research has been supported by Brno University of Technology, specific research plan no. FSI-S-17-4464 and by the grant 17-03224S of the Czech Science Foundation. The author would like to thank two anonymous reviewers for their helpful and constructive comments.

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Authors and Affiliations

  1. Institute of Mathematics, FME, Brno University of Technology, Technická 2, 61669, Brno, Czech Republic

    Pavel Řehák

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  1. Pavel Řehák
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Correspondence to Pavel Řehák .

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Editors and Affiliations

  1. Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO, USA

    Martin Bohner

  2. Institute for Analysis, CfD, Dresden University of Technology, Dresden, Germany

    Stefan Siegmund

  3. Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Brno, Czech Republic

    Roman Šimon Hilscher

  4. Department of Mathematics, University of West Bohemia, Pilsen, Czech Republic

    Petr Stehlík

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Řehák, P. (2020). A Note on Transformations of Independent Variable in Second Order Dynamic Equations. In: Bohner, M., Siegmund, S., Šimon Hilscher, R., Stehlík, P. (eds) Difference Equations and Discrete Dynamical Systems with Applications. ICDEA 2018. Springer Proceedings in Mathematics & Statistics, vol 312. Springer, Cham. https://doi.org/10.1007/978-3-030-35502-9_15

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