Sharp oscillation and nonoscillation tests for delay dynamic equations


KARPUZ B.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.42, no.9, pp.2993-3001, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 9
  • Publication Date: 2019
  • Doi Number: 10.1002/mma.5558
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2993-3001
  • Keywords: dynamic equation, nonoscillation, oscillation, time scale
  • Dokuz Eylül University Affiliated: Yes

Abstract

In this paper, we give new sufficient conditions for both oscillation and nonoscillation of the delay dynamic equation x Delta(t)+p(t)x(tau(t))=0fort is an element of[t0,infinity)T,where p is an element of Crd([t0,infinity)T,R0+) and tau is an element of Crd([t0,infinity)T,T) satisfy tau(t) <= sigma(t) for all large t and limt ->infinity tau(t)=infinity. As an important corollary, we obtain the time scale invariant integral condition for nonoscillation: integral tau(t)sigma(t)p(eta)Delta eta <= 1e for all large t. Also, with some examples, we show that newly presented results are sharp.