四阶微分方程的迭代解

白占兵

doi:10.12341/jssms09480

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系统科学与数学 ›› 2007, Vol. 27 ›› Issue (4) : 555-562. DOI: 10.12341/jssms09480

论文

四阶微分方程的迭代解

白占兵

作者信息 +

The Iterative Solution for some Fourth-Order DifferentialEquations

Bai Zhanbing

Author information +

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摘要

利用一个构造性的方法,在假设边值问题存在上解

α

和下解

β

,满足

β \leq α

的前提下, 给出了两个单调序列它们一致收敛于如下两类边值问题的极值解

u^{(4)} (x) - M u^{″} (x) = f (x, u (x), u^{'} (x), u^{″} (x), u^{‴} (x)), 0 < x < 1,

u (0) = u^{'} (1) = u^{″} (0) = u^{‴} (1) = 0;

u^{(4)} (x) - M u^{″} (x) = g (x, u (x), u^{'} (x), u^{″} (x)), 0 < x < 1,

u (0) = u^{'} (1) = u^{″} (0) = u^{‴} (1) = 0.

Abstract

In this paper we describe a constructive method which yields two monotone sequences that converge uniformly to extremal solutions to the following boundary value problems

u^{(4)} (x) - M u^{″} (x) = f (x, u (x), u^{'} (x), u^{″} (x), u^{‴} (x)), 0 < x < 1,

u (0) = u^{'} (1) = u^{″} (0) = u^{‴} (1) = 0,

and

u^{(4)} (x) - M u^{″} (x) = g (x, u (x), u^{'} (x), u^{″} (x)), 0 < x < 1,

u (0) = u^{'} (1) = u^{″} (0) = u^{‴} (1) = 0,

if there exist an upper solution

β

and a lower solution

α

with

β \leq α

导出引用

白占兵. 四阶微分方程的迭代解. 系统科学与数学, 2007, 27(4): 555-562. https://doi.org/10.12341/jssms09480

Bai Zhanbing. The Iterative Solution for some Fourth-Order DifferentialEquations. Journal of Systems Science and Mathematical Sciences, 2007, 27(4): 555-562 https://doi.org/10.12341/jssms09480

中图分类号： 34B15

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收稿日期	修回日期	出版日期
2005-10-24	1900-01-01	2007-08-25
发布日期
2007-08-25

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