| 中立型时滞微分方程非振动解的存在性与迭代逼近 |
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| 引用本文： | 马连,刘桂荣. 中立型时滞微分方程非振动解的存在性与迭代逼近[J]. 太原师范学院学报(自然科学版), 2010, 9(3) |
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| 作者姓名： | 马连 刘桂荣 |
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| 作者单位： | 山西大学,数学科学学院,山西,太原,030006 |
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| 基金项目： | 数学天元基金，山西省青年科技基金 |
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| 摘 要： | 讨论下列高阶中立型时滞微分方程dndtn[x(t)+cx(t-τ)]+∑n-1(-1)n-i+1 didtihi(t,x(σ1(t)),x(σ2(t)),…,x(σk(t)))+(-1)n+1 f(t,x(τ1(t)),x(τ2(t)),…,x(τk(t)))=g(t),t≥t0.利用压缩映象原理,得到上述方程非振动解存在性的充分条件,并给出收敛于该方程非振动解的一个Mann-型迭代逼近序列,最后进行相应的误差估计.
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| 关 键 词： | 中立型时滞微分方程 非振动解 压缩映象原理 |
Existence and Iterative Approximations of Nonoscillatory Solutions of Order Neutral Delay Differential Equations |
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| Ma Lian,Liu Guirong. Existence and Iterative Approximations of Nonoscillatory Solutions of Order Neutral Delay Differential Equations[J]. Journal of Taiyuan Normal University:Natural Science Edition, 2010, 9(3) |
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| Authors: | Ma Lian Liu Guirong |
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| Affiliation: | Ma Lian Liu Guirong(School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China) |
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| Abstract: | Using contraction mapping principle,the existence of nonscillatory solutions of a class of higher order neutral delay differential equation is obtained.In addition,we construct a Mann-typeiterative approximation scheme for these nonoscillatory solutions and estabish several error estimates between the approximate solutions and the nonoscillatory solutions. |
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| Keywords: | neutral delay differential equation nonoscillatory solution contraction mapping principle |
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