Necessary and sufficient conditions for oscillation of neutral equations with real coefficients

Farrell, Kate

doi:10.1016/0022-247x(89)90106-6

Cited by 10 publications

(11 citation statements)

References 5 publications

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“…When n = 1, system (1) under the hypothesis (H) reduces to a scalar neutral delay differential equation with positive and negative coefficients whose oscillatory behavior has been investigated in [2], [3] and [7]. In this paper we study the oscillation of systems of the form (l), (2) and we illustrate our results which substantially improve some known results for the scalar case.…”

Section: Introductionsupporting

confidence: 62%

Oscillation of Systems of Neutral Equations with Variable Coefficients

Georgiou

Qian

1992

Mathematische Nachrichten

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Consider the system of the neutral delay differential equationswhere P ( t ) = (pij(t)), Q(t) = (qij(t)) and R ( t ) = (rij(t)) are n x n matrices for t 0 and the delays T, a and e are nonnegative numbers. We obtain sufficient conditions for the oscillation of all solutions of (1) under the following hypotheses: and IntroductionConsider the system of the neutral delay differential equations where P ( t ) = ( p i j ( t ) ) , Q ( t ) = (qij(t)) and R(t) = (rij(t)) are n x n continuous matrices for t 2 0 and the delays T , O and Q are nonnegative numbers.

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Section: Introductionsupporting

confidence: 62%

Oscillation of Systems of Neutral Equations with Variable Coefficients

Georgiou

Qian

1992

Mathematische Nachrichten

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“…Necessary and sufficient conditions (in terms of the characteristic equation) for the oscillation of all solutions of first order neutral differential equations have been obtained by Sficas and Stavroulakis [22], Grove, Ladas and Meimaridou [13], Kulenovic, Ladas and Meimaridou [16], Grammatikopoulos, Sficas and Stavroulakis [10], Farrell [7], and Grammatikopoulos and Stavroulakis [11,12]. Necessary and sufficient conditions for the oscillation of higher order equations have been obtained by Ladas, Sficas and Stavroulakis [18], Ladas, Partheniadis and Sficas [17], and Wang [25].…”

Section: D" [ (E 3 ) ^( 0 ŵmentioning

confidence: 99%

“…[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). Indeed, this is derived by comparing elements of the set A + (x) (respectively A~(x)) in each case.…”

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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“…In [7] it was shown that if (2) holds, if The oscillation of neutral delay differential equations with positive and negative constant coefficients was studied in [3], and [4].…”

Section: ?-•Oomentioning

confidence: 99%