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, cilt.37, sa.8, ss.1219-1231, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 37 Sayı: 8
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1002/mma.2884
  • Dergi Adı: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1219-1231
  • Anahtar Kelimeler: time scales, second-order nonlinear dynamic equations, asymptotic behavior, positive and negative coefficients, oscillation, nonoscillation, NONOSCILLATORY SOLUTIONS, DIFFERENTIAL-EQUATIONS, OSCILLATION CRITERIA, EXISTENCE
  • Dokuz Eylül Üniversitesi Adresli: Hayır

Özet

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.