Oscillation of third-order nonlinear delay difference equations

AKTAŞ M. F. , Tiryaki A., Zafer A.

TURKISH JOURNAL OF MATHEMATICS, vol.36, no.3, pp.422-436, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 3
  • Publication Date: 2012
  • Doi Number: 10.3906/mat-1010-67
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.422-436
  • Keywords: Difference equation, Delay, Third order, Oscillation, Nonoscillation, Riccati transformation, CRITERIA, THEOREMS
  • Middle East Technical University Affiliated: Yes


Third-order nonlinear difference equations of the form Delta(c(n)Delta(d(n)Delta x(n))) p(n)Delta x(n+1) + q(n)f (x(n-sigma)) = n >= n(0) are considered. Here, {c(n)}, {d(n)}, {p(n)} and {q(n)} are sequences of positive real numbers for n(0) is an element of N, f is a continuous function such that f(u)/u >= K > 0 for u not equal 0. By means of a Riccati transformation technique we obtain some new oscillation criteria. Examples are given to illustrate the importance of the results.