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Asymptotic Properties of Nonoscillatory Solutions of Third-Order Delay Difference Equations

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Differential and Difference Equations with Applications (ICDDEA 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 230))

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Abstract

We study a third-order delay trinomial difference equation. We transform this equation to a binomial third-order difference equation with quasidifferences. Using comparison theorems with a certain first order delay difference equation we establish results on asymptotic properties of nonoscillatory solutions of the studied equation. We give an easily verifiable criterium which ensures that all nonoscillatory solutions tend to zero.

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Acknowledgements

This work was partially supported by the Ministry of Science and Higher Education of Poland (04/43/DSPB/0090).

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Authors and Affiliations

  1. Institute of Mathematics, Poznań University of Technology, Piotrowo 3A, 60-965, Poznań, Poland

    Alina Gleska & Małgorzata Migda

Authors
  1. Alina Gleska
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  2. Małgorzata Migda
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Corresponding author

Correspondence to Małgorzata Migda .

Editor information

Editors and Affiliations

  1. Departamento de Ciências Exactas e Engenharia, Academia Militar, Amadora, Portugal

    Sandra Pinelas

  2. Facultad de Matemáticas, Universidad de Sevilla, Sevilla, Spain

    Tomás Caraballo

  3. Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan, Hubei, China

    Peter Kloeden

  4. Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, Tennessee, USA

    John R. Graef

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Gleska, A., Migda, M. (2018). Asymptotic Properties of Nonoscillatory Solutions of Third-Order Delay Difference Equations. In: Pinelas, S., Caraballo, T., Kloeden, P., Graef, J. (eds) Differential and Difference Equations with Applications. ICDDEA 2017. Springer Proceedings in Mathematics & Statistics, vol 230. Springer, Cham. https://doi.org/10.1007/978-3-319-75647-9_27

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