Oscillation in First Order Neutral Differential Equations with "Integrally Small" Coefficients

Yu, Jun; Yan, J.R.

doi:10.1006/jmaa.1994.1362

Cited by 25 publications

(9 citation statements)

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“…(3.18) when 3/2 < β 2. Thus our condition (3.11) is better than condition (11) in [14], and so Theorem 3.2 and Theorem 3.3 improve and extend Theorem 1 and Theorem 3 in [14], respectively.…”

Section: This Implies That −Z(t) Is a Positive Solution Of The Inequamentioning

confidence: 71%

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Oscillation and Nonoscillation of Neutral Differential Equations with Positive and Negative Coefficients

Luo¹,

Shen²

2004

Czechoslovak Mathematical Journal

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Section: This Implies That −Z(t) Is a Positive Solution Of The Inequamentioning

confidence: 71%

“…Remark 3.2. It should be noted that condition (11) in [14] is not satisfied for Eq. (3.18) when 3/2 < β 2.…”

Section: This Implies That −Z(t) Is a Positive Solution Of The Inequamentioning

confidence: 99%

Oscillation and Nonoscillation of Neutral Differential Equations with Positive and Negative Coefficients

Luo¹,

Shen²

2004

Czechoslovak Mathematical Journal

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“…Recently Li and Saker [22] considered the equation (1.1) when a(t) = 1 and given some finite sufficient conditions for oscillation of all solutions and applied these results to the logistic neutral delay differential equations. For further oscillation results when (1.5) does not hold we refer the reader to the articles by Yu [26,27] and Yu et al [29,30,31]. Our aim in this paper in Section 2 is to give some new integral sufficient conditions for oscillation of all solutions of equation (1.1) and show that the combined growth of P and Q without the condition (1.8) in the linear case can give oscillation even when (1.5) and (1.6) fail.…”

Section: X(t) = φ(T) For T ∈ [T 1 − ρ T 1 ] (14)mentioning

confidence: 99%

“…Acknowledgement The authors thanks the referee for his helpful suggestions and his excellent list of the references [26,27,29,30,31].…”

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confidence: 99%

Oscillation of Solutions to Nonlinear Neutral Delay Differential Equations

Saker¹,

Kubiaczyk²

2002

Journal of Applied Analysis

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Abstract. In this paper we shall consider the nonlinear neutral delay differential equations with variable coefficients. Some new sufficient conditions for oscillation of all solutions are obtained. Our results extend and improve some of the well known results in the literature. Some examples are considered to illustrate our main results. The neutral logistic equation with variable coefficients is considered to give some new sufficient conditions for oscillation of all positive solutions about its positive steady state.

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“…To see this, observe that Note that if we choose f t ≡ 0 in Example 4.2, then (3.1) will not be satisfied. We also remark that by applying Theorem 4 in [18], we see that all solutions of (4.3) are oscillatory. Therefore, Example 4.2 demonstrates the persistence of oscillation of all solutions of (4.3) under the impulsive perturbations (4.4).…”

Section: Lemma 25 Consider the Impulsive Differential Inequalitymentioning

confidence: 94%