Sharp oscillation and nonoscillation tests for delay dynamic equations

KARPUZ B.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, cilt.42, sa.9, ss.2993-3001, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 9
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1002/mma.5558
  • Dergi Adı: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2993-3001
  • Anahtar Kelimeler: dynamic equation, nonoscillation, oscillation, time scale
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

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.