• Title, Summary, Keyword: asymptotic behavior

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ASYMPTOTIC BEHAVIOR OF HIGHER ORDER DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENT

  • Yang, Yitao;Meng, Fanwei
    • Journal of applied mathematics & informatics
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    • v.28 no.1_2
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    • pp.333-343
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    • 2010
  • The asymptotic behavior of solutions of higher order differential equations with deviating argument $$(py^{(n-1)}(t))'\;+\;\sum\limits_{i=1}^{n-1}ci(t)y^{(i-1)}(t)\;=\;f\[t,\;y(t),\;y'(t),\;{\ldots},\;y^{(n-1)}(t),\;y(\phi(t)),\;y'(\phi(t)),\;{\ldots},\;y^{(n-1)}\;(\phi(t))\]\;\;\;\;(1)$$ $t\;{\in}\;[0,\;\infty)$ is studied. Our technique depends on an integral inequality containing a deviating argument. From this we obtain some sufficient conditions under which all solutions of Eq.(1) have some asymptotic behavior.

OSCILLATORY AND ASYMPTOTIC BEHAVIOR OF SECOND ORDER NONLINEAR DIFFERENTIAL INEQUALITY WITH PERTURBATION

  • Zhang, Quanxin;Song, Xia
    • Journal of applied mathematics & informatics
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    • v.29 no.1_2
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    • pp.475-483
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    • 2011
  • In this paper, we study the oscillatory and asymptotic behavior of a class of second order nonlinear differential inequality with perturbation and establish several theorems by using classification and analysis, which develop and generalize some known results.

Asymptotic cell loss decreasing rate in an ATM multiplexer loaded with heterogeneous on-off sources

  • Choi, Woo-Yong;Jun, Chi-Hyuck
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • pp.543-546
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    • 1996
  • Recently, some research has been done to analyze the asymptotic behavior of queue length distribution in ATM (Asynchronous Transfer Mode) multiplexer. In this paper, we relate this asymptotic behavior with the asymptotic behavior of decreasing cell loss probability when the buffer capacity is increased. We find with reasonable assumptions that the asymptotic rate of queue length distribution is the same as that of decreasing cell loss probability. Even under different priority control schemes and traffic classes, we find that this asymptotic rate of the individual cell loss probability of each traffic class does not change. As a consequence, we propose the upper bound of cell loss probability of each traffic class when a priority control scheme is employed. This bound is computationally feasible in a real-time. The numerical examples will be provided to validate this finding.

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Asymptotic behavior of ideals relative to injective A-modules

  • Song, Yeong-Moo
    • Communications of the Korean Mathematical Society
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    • v.10 no.3
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    • pp.491-498
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    • 1995
  • This paper is concerned with an asymptotic behavior of ideals relative to injective modules ove the commutative Noetherian ring A : under what conditions on A can we show that $$\bar{At^*}(a,E)=At^*(a,E)$?

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ASYMPTOTIC STABILITY OF COMPETING SPECIES

  • Kim, June Gi
    • Korean Journal of Mathematics
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    • v.4 no.1
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    • pp.39-43
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    • 1996
  • Large-time asymptotic behavior of the solutions of interacting population reaction-diffusion systems are considered. Polynomial stability was proved.

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UNIFORMLY LIPSCHITZ STABILITY AND ASYMPTOTIC BEHAVIOR OF PERTURBED DIFFERENTIAL SYSTEMS

  • Choi, Sang Il;Goo, Yoon Hoe
    • Journal of the Chungcheong Mathematical Society
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    • v.29 no.3
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    • pp.429-442
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    • 2016
  • In this paper we show that the solutions to the perturbed differential system $$y^{\prime}=f(t,y)+{\int}_{to}^{t}g(s,y(s),Ty(s))ds$$ have uniformly Lipschitz stability and asymptotic behavior by imposing conditions on the perturbed part $\int_{to}^{t}g(s,y(s),Ty(s))ds$ and the fundamental matrix of the unperturbed system y' = f(t, y).