Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2011, Number 1 (2011), Article ID 709427, 15 pages.
Asymptotic Convergence of the Solutions of a Discrete Equation with Two Delays in the Critical Case
A discrete equation with two integer delays and is considered for . We assume , where , and . Criteria for the existence of strictly monotone and asymptotically convergent solutions for are presented in terms of inequalities for the function . Results are sharp in the sense that the criteria are valid even for some functions with a behavior near the so-called critical value, defined by the constant . Among others, it is proved that, for the asymptotic convergence of all solutions, the existence of a strictly monotone and asymptotically convergent solution is sufficient.
Abstr. Appl. Anal., Volume 2011, Number 1 (2011), Article ID 709427, 15 pages.
First available in Project Euclid: 12 August 2011
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Berezansky, L.; Diblík, J.; Růžičková, M.; Šutá, Z. Asymptotic Convergence of the Solutions of a Discrete Equation with Two Delays in the Critical Case. Abstr. Appl. Anal. 2011 (2011), no. 1, Article ID 709427, 15 pages. doi:10.1155/2011/709427. https://projecteuclid.org/euclid.aaa/1313171420