Oscillation of fourth-order nonlinear neutral delay dynamic equations

Date

2015-04-01

Author

Grace, S. R.
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

214
views

0
downloads

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.

Subject Keywords

Oscillation, Neutral, Time scales, Fourth-order

URI

https://hdl.handle.net/11511/55038

Journal

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

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 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 third-order nonlinear delay difference equations AKTAŞ, MUSTAFA FAHRİ; Tiryaki, Aydin; Zafer, Ağacık (2012-01-01) 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.
Oscillatory behavior of integro-dynamic and integral equations on time scales Grace, S. R.; Zafer, Ağacık (2014-02-01) By making use of asymptotic properties of nonoscillatory solutions, the oscillation behavior of solutions for the integro-dynamic equation
Oscillation criteria for third-order nonlinear functional differential equations AKTAŞ, MUSTAFA FAHRİ; Tiryaki, A.; Zafer, Ağacık (Elsevier BV, 2010-07-01) In this work, we are concerned with oscillation of third-order nonlinear functional differential equations of the form

Citation Formats

S. R. Grace and A. Zafer, “Oscillation of fourth-order nonlinear neutral delay dynamic equations,” HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, pp. 331–339, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/55038.