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Hyers–Ulam Stability for a Type of Discrete Hill Equation

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Abstract

We establish the Hyers–Ulam stability of a second-order linear Hill-type h-difference equation with a periodic coefficient. Using results from first-order h-difference equations with periodic coefficient of arbitrary order, both homogeneous and non-homogeneous, we also establish a Hyers–Ulam stability constant. Several interesting examples are provided. As a powerful application, we use the main result to prove the Hyers–Ulam stability of a certain third-order h-difference equation with periodic coefficients of one form.

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Acknowledgements

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

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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, Okayama University of Science, Okayama, 700-0005, Japan

    Masakazu Onitsuka

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  1. Douglas R. Anderson
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  2. Masakazu Onitsuka
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Both authors contributed equally to the results in this paper.

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Correspondence to Douglas R. Anderson.

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Anderson, D.R., Onitsuka, M. Hyers–Ulam Stability for a Type of Discrete Hill Equation. Results Math 79, 68 (2024). https://doi.org/10.1007/s00025-023-02097-w

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