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


KARPUZ B.

APPLIED MATHEMATICS AND COMPUTATION, vol.215, no.6, pp.2174-2183, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 215 Issue: 6
  • Publication Date: 2009
  • Doi Number: 10.1016/j.amc.2009.08.013
  • Journal Name: APPLIED MATHEMATICS AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2174-2183
  • Keywords: Asymptotic behaviour, Bounded solutions, Dynamic equations, Higher-order, Nonoscillation, Oscillation, Time scales, NONOSCILLATORY SOLUTIONS, DIFFERENTIAL-EQUATIONS, EXISTENCE, OSCILLATION
  • Dokuz Eylül University Affiliated: No

Abstract

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. (C) 2009 Elsevier Inc. All rights reserved.