| 二阶非线性泛函微分方程解的振动性与渐近性 |
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| 引用本文： | 赵敏之,赵智国. 二阶非线性泛函微分方程解的振动性与渐近性[J]. 湖南文理学院学报(自然科学版), 2005, 17(2): 8-10,19 |
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| 作者姓名： | 赵敏之 赵智国 |
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| 作者单位： | 湖南商务职业技术学院,湖南,长沙,410205;中国人民保险公司湖南分公司,信息技术处,湖南,长沙,410008 |
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| 摘 要： | 讨论了两类二阶非线性泛函微分方程(a(t).(y'(t))σ)' q(t)f(y(τ(t)))g(y'(t))=0,(a(t).(y'(t))σ)' q(t)F(y(t),y(τ(t))g(y'(t))=0,其中t≥to,σ为正常数,当t≥to时a(t)>0,q(t)≥0,且q(t)不最终恒为0,τ'(t)>0,且limt→ ∞τ(t)= ∞.利用一些分析的技巧,得到了这两类方程的解振动与渐近性的充分性判据,所获结果可分别应用于σ=奇/奇与σ=偶/奇的情形.改进并推广了已有文献中的相应结论.
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| 关 键 词： | 泛函微分方程 振动 渐近性 |
| 文章编号： | 1672-6146(2005)02-0008-03 |
| 修稿时间： | 2005-01-11 |
Oscillatory and Asymptotic Behavior of Solutions of Second Order Nonlinear Functional Differential Equations |
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| ZHAO Min-zhi,ZHAO Zhi-guo. Oscillatory and Asymptotic Behavior of Solutions of Second Order Nonlinear Functional Differential Equations[J]. Journal of Hunan University of Arts and Science:Natural Science Edition, 2005, 17(2): 8-10,19 |
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| Authors: | ZHAO Min-zhi ZHAO Zhi-guo |
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| Abstract: | The oscillation and asymptotic behavior of second order nonlinear functional differential equations was discussed, and some new sufficient conditions were established for the oscillatory and asymptotic properties of solutions for these equations, which extended and improved the corresponding results in many known literatures. |
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| Keywords: | Functional differential equation Oscillation Asymptotic behavior. |
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