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Asymptotic Convergence of the Solutions of a Dynamic Equation on Discrete Time Scales
Joint Authors
Šmarda, Zdenĕk
Šutá, Z.
Růžičková, Miroslava
Diblík, Josef
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-20, 20 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-01-03
Country of Publication
Egypt
No. of Pages
20
Main Subjects
Abstract EN
The paper investigates a dynamic equation Δy(tn)=β(tn)[y(tn−j)−y(tn−k)] for n→∞, where k and j are integers such that k>j≥0, on an arbitrary discrete time scale T:={tn} with tn∈ℝ, n∈ℤn0−k∞={n0−k,n0−k+1,…}, n0∈ℕ, tn We assume β:T→(0,∞). It is proved that, for the asymptotic convergence of all solutions, the existence of an increasing and asymptotically convergent solution is sufficient. Therefore, the main attention is paid to the criteria for the existence of an increasing solution asymptotically convergent for n→∞. The results are presented as inequalities for the function β. Examples demonstrate that the criteria obtained are sharp in a sense.
American Psychological Association (APA)
Diblík, Josef& Růžičková, Miroslava& Šmarda, Zdenĕk& Šutá, Z.. 2012. Asymptotic Convergence of the Solutions of a Dynamic Equation on Discrete Time Scales. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-20.
https://search.emarefa.net/detail/BIM-482432
Modern Language Association (MLA)
Diblík, Josef…[et al.]. Asymptotic Convergence of the Solutions of a Dynamic Equation on Discrete Time Scales. Abstract and Applied Analysis No. 2012 (2012), pp.1-20.
https://search.emarefa.net/detail/BIM-482432
American Medical Association (AMA)
Diblík, Josef& Růžičková, Miroslava& Šmarda, Zdenĕk& Šutá, Z.. Asymptotic Convergence of the Solutions of a Dynamic Equation on Discrete Time Scales. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-20.
https://search.emarefa.net/detail/BIM-482432
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-482432