| 2n阶Lidstone边值问题正解的逐次迭代 |
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| 引用本文： | 姚庆六.2n阶Lidstone边值问题正解的逐次迭代[J].应用泛函分析学报,2006,8(2):110-117. |
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| 作者姓名： | 姚庆六 |
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| 作者单位： | 南京财经大学应用数学系,江苏,南京,210003 |
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| 摘 要： | 研究了2n阶Lidstone边值问题正解的逐次迭代,其中非线性项依赖于所有偶数阶导数.通过考察非线性项在某些有国介集合上的“高度”并利用单调迭代方法构造了一个逐次迭代程序.这个迭代程序从一个多项式开始并且是可行的.使用这个结论获得了m个正解的迭代方法,其中m是一个任意的自然数.
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| 关 键 词： | Lidstone边值问题 高阶常微分方程 正解 逐次迭代 |
| 文章编号： | 1009-1327（2006）02-0110-08 |
| 收稿时间： | 2005-06-15 |
| 修稿时间： | 2005年6月15日 |
Successive Iteration of Positive Solution to a 2nth Lidstone Boundary Value Problem |
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| YAO Qing-liu.Successive Iteration of Positive Solution to a 2nth Lidstone Boundary Value Problem[J].Acta Analysis Functionalis Applicata,2006,8(2):110-117. |
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| Authors: | YAO Qing-liu |
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| Abstract: | We study the successive iteration of positive solution for a 2nth Lidstone boundary value problem where the nonlinear term depends on all even-order derivatives. By considering the "heights" of nonlinear term on some bounded sets and applying monotone iterative technique we construct a successive iterative process. This iterative process starts off with a polynomial and is feasible. Applying this result we obtain the iterative method of m positive solutions where m is an arbitrary natural number. |
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| Keywords: | Lidstone boundary value problem higher-order ordinary differential equation positive solution successive iteration |
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