| 一类奇摄动三阶非线性微分方程的两点边值问题 |
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| 引用本文： | 李晓琴,余赞平,周哲彦.一类奇摄动三阶非线性微分方程的两点边值问题[J].漳州师院学报,2010(1):31-36. |
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| 作者姓名： | 李晓琴 余赞平 周哲彦 |
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| 作者单位： | 福建师范大学数学与计算机科学学院,福建福州350007 |
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| 摘 要： | 本文研究如下一类带有小参数的三阶非线性微分方程两点边值问题{εym=f（t,y,y′,y′′ε）,a〈t〈b y（a）=A（ε） y′′（a）=C（ε）y（b）B（ε）的解的高阶渐近展开,并利用压缩映像原理,证明了解的存在性并得到了解的高阶误差估计.
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| 关 键 词： | 非线性微分方程 两点边值问题 高阶展开 |
A Class Two Point Boundary Value Problem with Singular Perturbation for Third-order Nonlinear Differential Equation |
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| LI Xiao-qin,YU Zan-ping,ZHOU Zhe-yan.A Class Two Point Boundary Value Problem with Singular Perturbation for Third-order Nonlinear Differential Equation[J].Journal of ZhangZhou Teachers College(Philosophy & Social Sciences),2010(1):31-36. |
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| Authors: | LI Xiao-qin YU Zan-ping ZHOU Zhe-yan |
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| Institution: | (School of Mathematics and Computer Science,Fujian Normal University,Fuzhou,Fujian 350007,China) |
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| Abstract: | This paper studies the higher-order expansion of the solution of a class of two point boundary value problems for third-order nonlinear differential equation with small parameter as following{εym=f（t,y,y′,y′′ε）,atb y（a）=A（ε） y′′（a）=C（ε）y（b）B（ε） Then using Banach contraction mapping principle,proves the existence of solution and obtains the error estimate of the solution. |
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| Keywords: | nonlinear differential equation two point boundary value problem higher-order expansion |
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