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Asymptotic Convergence of the Solutions of a Discrete Equation with Two Delays in the Critical Case
Joint Authors
Šutá, Z.
Berezansky, Leonid
Růžičková, Miroslava
Diblík, Josef
Source
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-06-30
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
A discrete equation Δy(n)=β(n)[y(n−j)−y(n−k)] with two integer delays k and j, k>j≥0 is considered for n→∞.
We assume β:ℤn0−k∞→(0,∞), where ℤn0∞={n0,n0+1,…}, n0∈ℕ and n∈ℤn0∞.
Criteria for the existence of strictly monotone and asymptotically convergent solutions for n→∞ are presented in terms of inequalities for the function β.
Results are sharp in the sense that the criteria are valid even for some functions β with a behavior near the so-called critical value, defined by the constant (k−j)−1.
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.
American Psychological Association (APA)
Berezansky, Leonid& Diblík, Josef& Růžičková, Miroslava& Šutá, Z.. 2011. Asymptotic Convergence of the Solutions of a Discrete Equation with Two Delays in the Critical Case. Abstract and Applied Analysis،Vol. 2011, no. 2011, pp.1-15.
https://search.emarefa.net/detail/BIM-492346
Modern Language Association (MLA)
Berezansky, Leonid…[et al.]. Asymptotic Convergence of the Solutions of a Discrete Equation with Two Delays in the Critical Case. Abstract and Applied Analysis No. 2011 (2011), pp.1-15.
https://search.emarefa.net/detail/BIM-492346
American Medical Association (AMA)
Berezansky, Leonid& Diblík, Josef& Růžičková, Miroslava& Šutá, Z.. Asymptotic Convergence of the Solutions of a Discrete Equation with Two Delays in the Critical Case. Abstract and Applied Analysis. 2011. Vol. 2011, no. 2011, pp.1-15.
https://search.emarefa.net/detail/BIM-492346
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-492346