| 一类n-阶m-点奇异边值问题的正解 |
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| 引用本文： | 郝新安,刘立山.一类n-阶m-点奇异边值问题的正解[J].系统科学与数学,2010,30(1):118-128. |
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| 作者姓名： | 郝新安 刘立山 |
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| 作者单位： | 曲阜师范大学数学科学学院,曲阜,273165 |
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| 基金项目： | 国家自然科学基金资助项目，高等学校博士点科研基金资助项目，曲阜师范大学博士科研启动经费 |
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| 摘 要： | 研究n-阶m-点奇异边值问题其中h(t)允许在t=0,t=1处奇异,f(t,v_0,v_1,…,v_(n-2))允许在v_i=0(i=0,1,…,n-2)处奇异.利用锥拉伸与压缩不动点定理得到了上述奇异边值问题正解的存在性.
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| 关 键 词： | 正解 n-阶m-点奇异边值问题 不动点定理. |
| 收稿时间： | 2008-5-26 |
POSITIVE SOLUTIONS FOR A CLASS OF N TH-ORDER M-POINT SINGULAR BOUNDARY VALUE PROBLEM |
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| HAO Xinan,LIU Lishan.POSITIVE SOLUTIONS FOR A CLASS OF N TH-ORDER M-POINT SINGULAR BOUNDARY VALUE PROBLEM[J].Journal of Systems Science and Mathematical Sciences,2010,30(1):118-128. |
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| Authors: | HAO Xinan LIU Lishan |
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| Institution: | School of Mathematical Sciences, Qufu Normal University, Qufu 273165 |
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| Abstract: | In this paper, by using Krasnosel'skill fixed point theorem,the existence result of positive solutions is established for the following $n$th-order $m$-point singularboundary value problem:$$\left\{\aligned& u^{(n)}(t)+h(t)f(t,u(t),u'(t),\cdots,u^{(n-2)}(t))=0,\ \ 0<t<1,\\& u(0)=u'(0)=\cdots=u^{(n-2)}(0)=0,\ u^{(n-2)}(1)=\sum_{i=1}^{m-2}k_{i}u^{(n-2)}(\xi_{i}), \endaligned\right.$$where $h(t)$ can be singular at $t=0,\ t=1$, $f(t,v_0,v_1,\cdots,v_{n-2})$ may also be singular at $v_{i}=0\ (i=0,1,\cdots,n-2)$. |
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| Keywords: | Positive solution nth-order m-point singular boundary value problem fixed point theorem |
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