Oscillation of third-order nonlinear delay difference equations

Date

2012-01-01

Author

AKTAŞ, MUSTAFA FAHRİ
Tiryaki, Aydin
Zafer, Ağacık

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

300
views

0
downloads

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.

Subject Keywords

Difference equation, Delay, Third order, Oscillation, Nonoscillation, Riccati transformation

URI

https://hdl.handle.net/11511/57946

Journal

TURKISH JOURNAL OF MATHEMATICS

DOI

https://doi.org/10.3906/mat-1010-67

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Oscillation criteria for even order neutral differential equations Zafer, Ağacık (1998-05-01) Oscillation criteria are given for even order neutral type differential equations of the following form
Oscillation of fourth-order nonlinear neutral delay dynamic equations Grace, S. R.; Zafer, Ağacık (2015-04-01) In this work we establish some new sufficient conditions for oscillation of fourth-order nonlinear neutral delay dynamic equations of the form (a(t)([x(t) - p(t) x(h(t))](Delta Delta Delta))(alpha))(Delta) + q(t)x(beta)(g(t)) = 0, t is an element of [t(0),infinity) T, where alpha and beta are quotients of positive odd integers with beta <= alpha.
Oscillation of higher order neutral type difference equations Zafer, Ağacık (1995-08-11) In this work we are concerned with oscillation of solutions of the neutral difference equation of the form
Oscillation of higher order nonlinear dynamic equations on time scales Grace, Said R; Agarwal, Ravi P; Zafer, Ağacık (Springer Science and Business Media LLC, 2012-5-23) Some new criteria for the oscillation of nth order nonlinear dynamic equations of the form x(Delta n) (t) + q (t) (x(sigma) (xi (t)))(lambda) = 0 are established in delay xi(t) a parts per thousand currency sign t and non-delay xi(t) = t cases, where n a parts per thousand yen 2 is a positive integer, lambda is the ratio of positive odd integers. Many of the results are new for the corresponding higher order difference equations and differential equations are as special cases.
Oscillation of nonlinear elliptic inequalities with p(x)-Laplacian ŞAHİNER, YETER; Zafer, Ağacık (2013-04-01) Sufficient conditions are obtained for the oscillation of solutions of half-linear and super-half-linear elliptic inequalities with p(x)-Laplacian. The results obtained are new even for the one-dimensional case.

Citation Formats

M. F. AKTAŞ, A. Tiryaki, and A. Zafer, “Oscillation of third-order nonlinear delay difference equations,” TURKISH JOURNAL OF MATHEMATICS, pp. 422–436, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/57946.