LONG-TIME BEHAVIOR OF POSITIVE SOLUTIONS OF A DIFFERENTIAL EQUATION WITH STATE-DEPENDENT DELAY

JOSEF DIBLIK

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LONG-TIME BEHAVIOR OF POSITIVE SOLUTIONS OF A DIFFERENTIAL EQUATION WITH STATE-DEPENDENT DELAY

机译：具有国家依赖延迟的微分方程正解的长时间行为

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摘要

The long-time behavior of positive solutions of a differential equation with state-dependent delay y(t) =-c(t)y(t-τ(t,y(t))), where c is a positive coefficient, is considered. Sufficient conditions are given for the existence of positive solutions bounded from below and from above by functions of exponential type. As a consequence, criteria for the existence of positive solutions are derived and their lower bounds are given. Relationships are discussed with the existing results on the existence of positive solutions for delayed differential equations.

机译：具有状态依赖性延迟y（t）= -c（t）y（t-τ（t，y（t））的微分方程的正解的长时间行为，其中c是正系数，是经过考虑的。通过指数类型的函数，给出了从下方和从上方界定的正溶液的存在的充分条件。因此，推导出阳性溶液存在的标准，并给出它们的下界。与存在的延迟微分方程存在正解的存在关系，讨论了关系。

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《Discrete and continuous dynamical systems▼hSeries S》 |2020年第1期|31-46|共16页
作者
JOSEF DIBLIK;
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作者单位

CEITEC - Central European Institute of Technology Brno University of Technology Brno Czech Republic;

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正文语种 eng
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关键词
Long-time behavior; time-dependent delay; exponential estimation of solutions; positive solution; monotone iterative method;

机译：长期行为;时间依赖的延迟;解决方案的指数估计;积极的解决方案;单调迭代方法;

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专利

1. Erratum: Asymptotic behavior of solutions to a system of differential equations with state-dependent delays (CAM (2009) 228 (226-230)) [J] . Wang L. Journal of Computational and Applied Mathematics . 2011,第11期

机译：勘误：具有状态依赖时滞的微分方程组解的渐近行为（CAM（2009）228（226-230））
2. Asymptotic behavior of solutions to a system of differential equations with state-dependent delays [J] . Wang L Journal of Computational and Applied Mathematics . 2009,第1期

机译：具有状态依赖时滞的微分方程组解的渐近行为
3. Existence of multiple positive periodic solutions for differential equation with state-dependent delays [J] . Han F, Wang QY Journal of Mathematical Analysis and Applications . 2006,第2期

机译：具有状态依赖时滞的微分方程的多个正周期解的存在性
4. Existence of three positive periodic solutions of nonlinear neutral functional differential equations with impulses and delays [C] . Yaping Ren 2011 International Conference on Multimedia Technology . 2011

机译：具脉冲和时滞的非线性中立型泛函微分方程三个正周期解的存在性。
5. Differential equations with state-dependent delay: Global Hopf bifurcation and smoothness dependence on parameters. [D] . Hu, Qingwen. 2008

机译：具有状态相关延迟的微分方程：全局Hopf分叉和平滑度对参数的依赖。
6. Delayed singularity formation for solutions of nonlinear partial differential equations in higher dimensions [O] . Fritz John 1976

机译：高维非线性偏微分方程解的延迟奇异性形成。
7. Retraction notice to: Asymptotic behavior of solutions to a system of differential equations with state-dependent delays CAM 228 (2009) pp. 226—230 [O] . Wang Lijuan 2011

机译：收回通知：具有状态依赖延迟的微分方程组解的渐近行为CAM 228（2009）pp.226—230
8. Estimation of Time- and State-Dependent Delays and Other Parameters in Functional Differential Equations [R] . Murphy, K. A. 1988

机译：泛函微分方程中时间和状态依赖时滞及其他参数的估计

LONG-TIME BEHAVIOR OF POSITIVE SOLUTIONS OF A DIFFERENTIAL EQUATION WITH STATE-DEPENDENT DELAY

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