Oscillations of Neutral Delay Differential Equations

Ladas, G.; Sficas, Y. G.

doi:10.4153/cmb-1986-069-2

Cited by 73 publications

(45 citation statements)

References 13 publications

(12 reference statements)

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“…COROLLARY Observed that in the case of the mixed type equations (cf. [20] The method of proof which we used to establish our main result is short (cf. [7]) and also has the advantage that it results in easily verifiable sufficient conditions for the oscillation of solutions to Equation (1).…”

Section: Applications and Examplesmentioning

confidence: 99%

Oscillations of higher order neutral differential equations

1992

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Consider the nth-order neutral differential equationwhere n> 1 , 8 = ± 1 , / , 31 are initial segments of natural numbers , p ( , T ; , a k 6 R and q k > 0 for i g / and k e 3T . Then a necessary and sufficient condition for the oscillation of all solutions of (E) is that its characteristic equation has no real roots. The method of proof has the advantage that it results in easily verifiable sufficient conditions (in terms of the coefficients and the arguments only) for the oscillation of all solutions of Equation (E).

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Section: Applications and Examplesmentioning

confidence: 99%

Oscillations of higher order neutral differential equations

1992

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“…The oscillatory behavior of neutral differential equations has been the subject of many recent investigations. See, for example [l]- [5], [8], and [12] and the references cited therein. The technique that we employ in the proof of Theorem 1 was initiated in [9] and [ 10] and had been used successfully in linear neutral autonomous equations.…”

Section: ) J-t{x(t) +Px(t -T)] + Q(t)x(t -mentioning

confidence: 99%

“…Let W be the set of all continuously differentiable solutions w(t) of (1) with the properties that (8) w(t) > 0 and w(t)<0 for all large t and lim w(t) = 0.…”

Section: ) J-t{x(t) +Px(t -T)] + Q(t)x(t -mentioning

confidence: 99%

Oscillations in neutral equations with periodic coefficients

Ladas¹,

Philos²,

Sficas³

1991

Proc. Amer. Math. Soc.

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Abstract.We obtain a necessary and sufficient condition for the oscillation of all solutions of the neutral delay differential equation:where p 6 R, Q e C [[0, oo), R+], Q is w-periodic with m > 0 , Q(t) ^ 0 for t ^ 0, and there exist positive integers nx and n2 such that z = nlu> and a = n2oj. More precisely we show that every solution of (1) oscillates if and only if every solution of an associated neutral equation with constant coefficients oscillates.

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“…A systematic development of oscillation theory of neutral equations was initiated by Ladas and Sficas [10].…”

Section: Introductionmentioning

confidence: 99%

“…Neutral delay differential equations appear in networks containing lossless transmission lines (as in high-speed computers where the lossless transmission lines are used to interconnect switching circuits), in the study of vibrating masses attached to an elastic bar and also in population dynamics (see Gopalsamy In fact, Zahariev and Baȋnov [11] seems to be the first paper dealing with oscillation of neutral equations. A systematic development of oscillation theory of neutral equations was initiated by Ladas and Sficas [10].…”

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confidence: 99%

On the oscillation of first‐order neutral delay differential equations with real coefficients

Al-Amri

2002

International Journal of Mathematics and Mathematical Sciences

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We prove sufficient conditions for the oscillation of all solutions of a scalar first-order neutral delay differential equationẋ(t)− cẋ(t − τ)+ n i=1 p i x(t − σ i ) = 0 for all 0 < c < 1, τ,σ i > 0, and p i ∈ R, i = 1, 2,...,n.2000 Mathematics Subject Classification: 34C15, 34K40.1. Introduction. The theory of neutral delay differential equations presents complications and the results which are true for neutral differential equations may not be true for nonneutral differential equations. Besides its theoretical interest, the study of oscillatory behaviour of solutions of neutral delay differential equations has some importance in applications. Neutral delay differential equations appear in networks containing lossless transmission lines (as in high-speed computers where the lossless transmission lines are used to interconnect switching circuits), in the study of vibrating masses attached to an elastic bar and also in population dynamics (see Gopalsamy In fact, Zahariev and Baȋnov [11] seems to be the first paper dealing with oscillation of neutral equations. A systematic development of oscillation theory of neutral equations was initiated by Ladas and Sficas [10].Ladas and Schultz [9] obtained a necessary and sufficient condition for oscillation of all solutions of the neutral delay differential equatioṅ

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Oscillations of Neutral Delay Differential Equations

Abstract: The oscillatory behavior of the solutions of the neutral delay differential equationwhere p, τ, and a are positive constants and Q ∊ C([t0, ∞), ℝ+), are studied.

Cited by 73 publications

References 13 publications

Oscillations of higher order neutral differential equations

Oscillations of higher order neutral differential equations

Oscillations in neutral equations with periodic coefficients

On the oscillation of first‐order neutral delay differential equations with real coefficients

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