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Hyers—Ulam Stability of Second-Order Linear Dynamic Equations on Time Scales

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Abstract

We investigate the Hyers—Ulam stability (HUS) of certain second-order linear constant coefficient dynamic equations on time scales, building on recent results for first-order constant coefficient time-scale equations. In particular, for the case where the roots of the characteristic equation are non-zero real numbers that are positively regressive on the time scale, we establish that the best HUS constant in this case is the reciprocal of the absolute product of these two roots. Conditions for instability are also given.

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Authors and Affiliations

  1. Department of Mathematics, Concordia College, Moorhead, MN, 56562, USA

    Douglas R. Anderson

  2. Department of Applied Mathematics, Kayama University of Science, Okayama, 700-0005, Japan

    Masakazu Onitsuka

Authors
  1. Douglas R. Anderson
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  2. Masakazu Onitsuka
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Corresponding author

Correspondence to Douglas R. Anderson.

Additional information

The second author was supported by JSPS KAKENHI Grant Number JP20K03668.

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Anderson, D.R., Onitsuka, M. Hyers—Ulam Stability of Second-Order Linear Dynamic Equations on Time Scales. Acta Math Sci 41, 1809–1826 (2021). https://doi.org/10.1007/s10473-021-0525-2

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  • DOI: https://doi.org/10.1007/s10473-021-0525-2

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