On the asymptotic behavior of the pantograph equations

Makay, Géza; Terjéki, József

doi:10.14232/ejqtde.1998.1.2

Cited by 23 publications

(21 citation statements)

References 3 publications

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“…Since this case has been already discussed by G. Makay and J. Terjéki in [14], we only verify that our following result is covered by the appropriate statement of [14]. (2.1), where a, b ∈ C((0, ∞)), |b(t)| ≤ −Qa(t) for a suitable Q > 0 and all t large enough and let (2.2) hold.…”

Section: Lemma 22 Consider Equation (21) Subject To the Same Assumpmentioning

confidence: 84%

“…The non-autonomous equation (1.1), where c is a negative function and p = 1, has been studied by G. Makay and J. Terjéki [14]. They showed that under some differentiable and monotonicity conditions imposed on c every solution x of (1.1) (with p = 1) is asymptotically logarithmically periodic, i.e., there is a periodic function ψ such that x e t − ψ(t) → 0 as t → ∞.…”

Section: Introductionmentioning

confidence: 99%

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On a linear differential equation with a proportional delay

Čermák

2007

Mathematische Nachrichten

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This paper deals with the delay differential equatioṅWe impose some growth conditions on c, under which we are able to give a precise description of the asymptotic properties of all solutions of this equation. Although we naturally have to distinguish the cases c eventually positive and c eventually negative, we show a certain resemblance between the asymptotic formulae corresponding to both cases. Moreover, using the transformation approach we generalize these results to the equation with a general form of a delay.

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Section: Lemma 22 Consider Equation (21) Subject To the Same Assumpmentioning

confidence: 84%

Section: Introductionmentioning

confidence: 99%

On a linear differential equation with a proportional delay

Čermák

2007

Mathematische Nachrichten

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“…Some results of the above-cited papers have been generalized in this direction by Heard [7], Makay and Terjéki [13], and in [2,3,4]. For further related results on the asymptotic behaviour of solutions, see, for example, Diblík [5,6], Iserles [8], or Krisztin [9].…”

Section: Y(t) = −A(t)y(t) +mentioning

confidence: 97%

Linear differential equations with unbounded delays and a forcingterm

Čermák

Kundrát

2004

Abstract and Applied Analysis

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The paper discusses the asymptotic behaviour of all solutions of the differential equa-, with a positive continuous function a, continuous functions b i , f , and n continuously differentiable unbounded lags. We establish conditions under which any solution y of this equation can be estimated by means of a solution of an auxiliary functional equation with one unbounded lag. Moreover, some related questions concerning functional equations are discussed as well.

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“…(1.2), relevant results or applications can be found, for example, in [5] or [6] for asymptotic estimation, variables' change in [7] and asymptotic behavior of the generalized pantograph differential equations in [9] or [12]. In both Eq.…”

Section: 2) Dx(t) = F (T X(t) Y(t))dtmentioning

confidence: 99%

On the General Decay Stability of Stochastic Differential Equations With Unbounded Delay

Meng¹,

Yin²

2012

Journal of the Korean Mathematical Society

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Abstract. This work focuses on the general decay stability of nonlinear stochastic differential equations with unbounded delay. A Razumikhintype theorem is first established to obtain the moment stability but without almost sure stability. Then an improved edition is presented to derive not only the moment stability but also the almost sure stability, while existing Razumikhin-type theorems aim at only the moment stability. By virtue of the M -matrix techniques, we further develop the aforementioned Razumikhin-type theorems to be easily implementable. Two examples are given for illustration.

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On the asymptotic behavior of the pantograph equations

Cited by 23 publications

References 3 publications

On a linear differential equation with a proportional delay

On a linear differential equation with a proportional delay

Linear differential equations with unbounded delays and a forcingterm

On the General Decay Stability of Stochastic Differential Equations With Unbounded Delay

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