| 三阶微分方程非线性边值问题的一致有效估计 |
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| 引用本文： | 王国灿.三阶微分方程非线性边值问题的一致有效估计[J].纺织高校基础科学学报,2009,22(3). |
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| 作者姓名： | 王国灿 |
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| 作者单位： | 大连交通大学,理学院,辽宁,大连,116028 |
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| 摘 要： | 利用积分算子和微分不等式技巧,讨论了三阶非线性微分方程非线性边值问题的奇摄动.以二阶Volterra型积分微分方程非线性边值问题的已知结果为基础,建立了三阶非线性边值问题的上下解方法.同时,构造适当的上下解,得到了解的存在性和一致有效估计.结果表明,这种技巧为其他三阶边值问题的研究提出了一种新的思路.
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| 关 键 词： | 三阶微分方程 上、下解方法 存在性和一致有效估计 |
Uniformly valid estimation of solution for nonlinear boundary problem of third order differential equation |
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| WANG Guo-can.Uniformly valid estimation of solution for nonlinear boundary problem of third order differential equation[J].Basic Sciences Journal of Textile Universities,2009,22(3). |
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| Authors: | WANG Guo-can |
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| Affiliation: | WANG Guo-can(School of Math.and Phys.,Dalian Jiaotong University,Dalian,Liangning 116028,China) |
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| Abstract: | Third order singularly perturbed nonlinear boundary value problem by means of differential inequality theories is studied.Based on the results of second order nonlinear boundary value problems of Volterra type integro-differential equation,the upper and lower solutions method of third order nonlinear boundary value problems was established.Specific upper and lower solutions were constructed,and existence and uniformly valid estimates of solutions under suitable condition were obtained.The result showed that... |
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| Keywords: | third order differential equation upper and lower solution method existence and uniformly valid estimation |
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