Asymptotic behaviour of bounded solutions of a class of higher-order neutral dynamic equations

In this paper, necessary and sufficient conditions for the asymptotic behaviour of all bounded solutions of a class of nonlinear higher-order neutral dynamic equations are stated related to various ranges of the coefficient associated with the neutral part, in one of which the coefficient is allowed...

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Bibliographic Details
Published in:Applied mathematics and computation 2009-11, Vol.215 (6), p.2174-2183
Main Author: Karpuz, Başak
Format: Article
Language:English
Subjects:
Asymptotic behaviour
Bounded solutions
Difference and functional equations, recurrence relations
Dynamic equations
Exact sciences and technology
Finite differences and functional equations
Higher-order
Mathematical analysis
Mathematics
Nonoscillation
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Oscillation
Sciences and techniques of general use
Time scales
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Summary:In this paper, necessary and sufficient conditions for the asymptotic behaviour of all bounded solutions of a class of nonlinear higher-order neutral dynamic equations are stated related to various ranges of the coefficient associated with the neutral part, in one of which the coefficient is allowed to oscillate and not tend to zero asymptotically. The new results improve and generalize the known results stated for difference equations and differential equations, and answer some problems left open for the case T = R for arbitrary time scales. Some certain examples, which the results in the literature fail to deliver an answer to, are given to illustrate the applicability and significance of the new results.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2009.08.013