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Oscillation criteria for even order neutral differential equations
Date
1998-05-01
Author
Zafer, Ağacık
Metadata
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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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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.
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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.
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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...
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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.