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General theorems for uniform asymptotic stability and boundedness in finitely delayed difference systems

Part of: Difference and functional equations Difference equations

Published online by Cambridge University Press:  27 May 2024

Youssef N. Raffoul Open the ORCID record for Youssef N. Raffoul [Opens in a new window]
Youssef N. Raffoul*
Affiliation:
Department of Mathematics, University of Dayton, 300 College Park, Dayton, OH, United States
*
e-mail: yraffoul1@udayton.edu
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Abstract

The paper deals with boundedness of solutions and uniform asymptotic stability of the zero solution. In our current undertaking, we aim to solve two open problems that were proposed by the author in his book Qualitative theory of Volterra difference equations (2018, Springer, Cham). Our approach centers on finding the appropriate Lyapunov functional that satisfies specific conditions, incorporating the concept of wedges.

Keywords

Finite delayLyapunov functionaluniform asymptotic stabilityuniform boundednessnonlinear

MSC classification

Primary: 39A13: Difference equations, scaling ($q$-differences) 39A23: Periodic solutions
Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 13
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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