| 二阶非线性常微分方程的三点边值问题的一个存在定理 |
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| 引用本文： | 姚庆六,江秀芬. 二阶非线性常微分方程的三点边值问题的一个存在定理[J]. 兰州大学学报(自然科学版), 2003, 39(1): 17-19 |
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| 作者姓名： | 姚庆六 江秀芬 |
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| 作者单位： | 南京经济学院应用数学系,江苏,南京,210003;南京经济学院,图书馆,江苏,南京,210003 |
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| 摘 要： | 获得了非线性二阶三点边值问题w^n(t) f(t,w(t)＝0.0≤t≤i;w（0）=0,αw（η）=w（I）的一个正解存在定理,其中0＜η＜1,0＜α＜l／η。在此,非线性项f既不是超线性又不是次线性的。结论是通过使用锥拉伸与锥压缩型Krasnosel’sskii不动点定理获得的。某些现有的存在性结论得到了改进和推广。
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| 关 键 词： | 非线性二阶三点边值问题 正解 存在性 Krasnosel’skii不动点定理 |
| 文章编号： | 0455-2059(2003)01-0017-03 |
| 修稿时间： | 2001-11-13 |
An existence theorem of three-point boundary value problem for second-order nonlinear ordinary differential equations |
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| YAO Qing-liu,JIANG Xiu-fen. An existence theorem of three-point boundary value problem for second-order nonlinear ordinary differential equations[J]. Journal of Lanzhou University(Natural Science), 2003, 39(1): 17-19 |
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| Authors: | YAO Qing-liu JIANG Xiu-fen |
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| Affiliation: | YAO Qing-liu1,JIANG Xiu-fen2 |
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| Abstract: | An existence theorem of positive solution is proved for a three-point boundary value problem of second-order nonlinear ordinary differential equation, where the nonlinearity may be neither superlinear nor sublinear. This result is obtained by using the Krasnosel'skii fixed point theorem of cone expansion-compression type. Some previous existence results are improved and generalized. |
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| Keywords: | nonlinear second-order three-point boundary value problem positive solution existence Krasnosel'skii fixed point theorem |
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