Oscillation criteria for even order neutral differential equations

Date

1998-05-01

Author

Zafer, Ağacık

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Oscillation criteria are given for even order neutral type differential equations of the following form

Subject Keywords

Neutral Differential Equation, Nonlinear, Higher Order, Oscillation, Eventually Positive Solution

URI

https://hdl.handle.net/11511/56376

Journal

APPLIED MATHEMATICS LETTERS

DOI

https://doi.org/10.1016/s0893-9659(98)00028-7

Collections

Department of Mathematics, Article

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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 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 second-order nonlinear differential equations with nonlinear damping Tiryaki, A; Zafer, Ağacık (2004-01-01) This paper is concerned with the oscillation of a class of general type second-order differential equations with nonlinear damping terms. Several new oscillation criteria are established for such a class of differential equations under quite general assumptions. Examples are also given to illustrate the results.
Bounded oscillation of nonlinear neutral differential equations of arbitrary order Yilmaz, YS; Zafer, Ağacık (2001-01-01) The paper is concerned with oscillation properties of n-th order neutral differential equations of the form
Oscillation of Higher-Order Neutral-Type Periodic Differential Equations with Distributed Arguments Dahiya, R. S.; Zafer, A. (Springer Science and Business Media LLC, 2007) We derive oscillation criteria for general-type neutral differential equations [x(t) +αx(t− τ) +βx(t +τ)](n) = δ b ax(t − s)dsq1(t,s) + δ d c x(t + s)dsq2(t,s) = 0, t ≥ t0, where t0 ≥ 0, δ = ±1, τ > 0, b>a ≥ 0, d>c ≥ 0, α and β are real numbers, the functions q1(t,s) : [t0,∞) × [a,b] → R and q2(t,s):[t0,∞) × [c,d] → R are nondecreasing in s for each fixed t, and τ is periodic and continuous with respect to t for each fixed s. In certain special cases, the results obtained generalize and improve s...

Citation Formats

A. Zafer, “Oscillation criteria for even order neutral differential equations,” APPLIED MATHEMATICS LETTERS, pp. 21–25, 1998, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/56376.