Necessary and sufficient conditions on the asymptotic behavior of second-order neutral delay dynamic equations with positive and negative coefficients


KARPUZ B.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.37, no.8, pp.1219-1231, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 8
  • Publication Date: 2014
  • Doi Number: 10.1002/mma.2884
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1219-1231
  • Keywords: time scales, second-order nonlinear dynamic equations, asymptotic behavior, positive and negative coefficients, oscillation, nonoscillation, NONOSCILLATORY SOLUTIONS, DIFFERENTIAL-EQUATIONS, OSCILLATION CRITERIA, EXISTENCE
  • Dokuz Eylül University Affiliated: No

Abstract

In this paper, we establish necessary and sufficient conditions for the solutions of a second-order nonlinear neutral delay dynamic equation with positive and negative coefficients to be oscillatory or tend to zero asymptotically. We consider three different ranges of the coefficient associated with the neutral part in one of which it is allowed to be oscillatory. Thus, our results improve and generalize the existing results in the literature to arbitrary time scales. Some examples on nontrivial time scales are also given. Copyright (c) 2013 John Wiley & Sons, Ltd.