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

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 cen...

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Bibliographic Details
Published in:Canadian mathematical bulletin 2024-12, Vol.67 (4), p.1046-1058
Main Author: Raffoul, Youssef N.
Format: Article
Language:English
Subjects:
Asymptotic properties
Difference equations
Stability
Theorems
Online Access:Get full text
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Summary: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.
ISSN:0008-4395
1496-4287
DOI:10.4153/S0008439524000353