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Lyapunov Functionals and Stability in Finite Delays Difference Equations

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Difference Equations, Discrete Dynamical Systems and Applications (ICDEA 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 287))

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Abstract

In this research we prove general theorems regarding the stability of the zero solution of a functional difference equation with finite delay. In the analysis we assume the existence of a Lyapunov functional that satisfies certain conditions. Results on finite delay difference equations using Lyapunov functions or functionals are scarce. We apply our results to finite delay difference equations and to Volterra difference equations with finite delays.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Dayton, Dayton, OH, 45469-2316, USA

    Youssef N. Raffoul

Authors
  1. Youssef N. Raffoul
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Correspondence to Youssef N. Raffoul .

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Editors and Affiliations

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

    Saber Elaydi

  2. Institut für Mathematik, Alpen-Adria Universität Klagenfurt, Klagenfurt, Austria

    Christian Pötzsche

  3. Department of Mathematics, West University of TimiÅŸoara, TimiÅŸoara, Romania

    Adina Luminiţa Sasu

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Raffoul, Y.N. (2019). Lyapunov Functionals and Stability in Finite Delays Difference Equations. In: Elaydi, S., Pötzsche, C., Sasu, A. (eds) Difference Equations, Discrete Dynamical Systems and Applications. ICDEA 2017. Springer Proceedings in Mathematics & Statistics, vol 287. Springer, Cham. https://doi.org/10.1007/978-3-030-20016-9_16

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