Abstract and Applied Analysis

Asymptotic Behavior of Solutions of Delayed Difference Equations

J. Diblík and I. Hlavičková

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Abstract

This contribution is devoted to the investigation of the asymptotic behavior of delayed difference equations with an integer delay. We prove that under appropriate conditions there exists at least one solution with its graph staying in a prescribed domain. This is achieved by the application of a more general theorem which deals with systems of first-order difference equations. In the proof of this theorem we show that a good way is to connect two techniques—the so-called retract-type technique and Liapunov-type approach. In the end, we study a special class of delayed discrete equations and we show that there exists a positive and vanishing solution of such equations.

Article information

Source
Abstr. Appl. Anal., Volume 2011, Number 1 (2011), Article ID 671967, 24 pages.

Dates
First available in Project Euclid: 12 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1313171421

Digital Object Identifier
doi:10.1155/2011/671967

Mathematical Reviews number (MathSciNet)
MR2817276

Zentralblatt MATH identifier
1217.39019

Citation

Diblík, J.; Hlavičková, I. Asymptotic Behavior of Solutions of Delayed Difference Equations. Abstr. Appl. Anal. 2011 (2011), no. 1, Article ID 671967, 24 pages. doi:10.1155/2011/671967. https://projecteuclid.org/euclid.aaa/1313171421


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