| 具状态时滞的高阶非线性微分方程正解正在性及分类 |
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| 引用本文： | 朱先阳,李永昆.具状态时滞的高阶非线性微分方程正解正在性及分类[J].数学研究,2004,37(3):238-244. |
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| 作者姓名： | 朱先阳 李永昆 |
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| 作者单位： | 云南大学数学系,昆明,650091 |
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| 基金项目： | theNationalNaturalScienceFoundationofPeople′sRepublicofChinaun dergrant 10 36 10 0 6andtheNaturalSciencesFoundationofYunnanProvinceundergrant 2 0 0 3A0 0 0 1M |
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| 摘 要： | 本文研究一类形如(r(t)x(n-1)(t))′+f(t,x(t),
x(Φ(t,x(t)))=0的具状态时滞的高阶非线性微分方程.
按照最终正解的量级给出了它们的分类及存在的充分条件.
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| 关 键 词： | 具状态时滞的微分方程 最终正解 渐近行为 不动点 |
Classification and Existence of Positive Solutions of Higher-order Nonlinear Differential Equations with State Dependent Delays |
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| Abstract.Classification and Existence of Positive Solutions of Higher-order Nonlinear Differential Equations with State Dependent Delays[J].Journal of Mathematical Study,2004,37(3):238-244. |
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| Authors: | Abstract |
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| Abstract: | A class of higher-order nonlinear differential equations with state dependent delays of the from(r(t)x(n-1)(t))′+f(t,x(t), x(Φ(t, x(t))))=0in the case when ∫∞0ds/r(s)=∞ is studied. Various classifications of their eventually positive solutions are given in terms of their asymptotic magnitudes, and necessary as well as sufficient conditions for the existence of these solutions are also provided. |
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| Keywords: | Differential equation with state dependent delay eventually positive solution asymptotic behavior fixed point theorem |
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