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Linearization for Difference Equations with Infinite Delay

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Advances in Discrete Dynamical Systems, Difference Equations and Applications (ICDEA 2021)

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Abstract

In this article, we construct a conjugacy map for a linear difference equation with infinite delay and corresponding nonlinear perturbation. We also prove that the conjugacy map is one-to-one with some additional conditions. As an application of our result, we show that the cases of (uniform) exponential dichotomy follow from our result.

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Acknowledgements

Author would like to thanks Prof. D. Dragičević for his valuable suggestions throughout the process of solving and writing this article. The Author is supported by Croatian Science Foundation under the project IP-2019-04-1239.

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Authors and Affiliations

  1. University of Rijeka, Rijeka, Croatia

    Lokesh Singh

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  1. Lokesh Singh
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Correspondence to Lokesh Singh .

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Editors and Affiliations

  1. Department of Mathematics, Trinity University, San Antonio, TX, USA

    Saber Elaydi

  2. University of Rhode Island, Kingston, RI, USA

    Mustafa R. S. Kulenović

  3. University of Sarajevo, Sarajevo, Bosnia and Herzegovina

    Senada Kalabušić

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Singh, L. (2023). Linearization for Difference Equations with Infinite Delay. In: Elaydi, S., Kulenović, M.R.S., Kalabušić, S. (eds) Advances in Discrete Dynamical Systems, Difference Equations and Applications. ICDEA 2021. Springer Proceedings in Mathematics & Statistics, vol 416. Springer, Cham. https://doi.org/10.1007/978-3-031-25225-9_21

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