| 一类奇异三阶三点边值问题的正解 |
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| 引用本文： | 吴红萍.一类奇异三阶三点边值问题的正解[J].数学研究及应用,2011,31(2):287-294. |
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| 作者姓名： | 吴红萍 |
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| 作者单位： | 西北师范大学数学与信息科学学院, 甘肃 兰州 730070 |
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| 基金项目： | 国家自然科学基金(Grant No.10871160). |
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| 摘 要： | In this paper,we study the existence of positive solutions for the nonlinear singular third-order three-point boundary value problemu （t） = λa（t）f（t,u（t））,u（0） = u （1） = u （η） = 0,where λ is a positive parameter and 0 ≤ η 1 2 .By using the classical Krasnosel’skii’s fixed point theorem in cone,we obtain various new results on the existence of positive solution,and the solution is strictly increasing.Finally we give an example.
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| 关 键 词： | positive solutions singular third-order three-point BVP fixed point theorem |
| 收稿时间： | 2009/4/10 0:00:00 |
| 修稿时间： | 2010/1/18 0:00:00 |
Positive Solutions to a Singular Third-Order Three-Point Boundary Value Problem |
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| Hong Ping WU.Positive Solutions to a Singular Third-Order Three-Point Boundary Value Problem[J].Journal of Mathematical Research with Applications,2011,31(2):287-294. |
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| Authors: | Hong Ping WU |
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| Institution: | College of Mathematics and Information Science, Northwest Normal University, Gansu 730070, P. R. China |
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| Abstract: | In this paper, we study the existence of positive solutions for the nonlinear singular third-order three-point boundary value problem $$\left\{\begin{array}{l}u'(t)=-\lambda a(t)f(t,u(t)),\\ u(0)=u'(1)=u'(\eta)=0,\end{array}\right.$$ where $\lambda $ is a positive parameter and $0\le\eta<\frac{1}{2}$. By using the classical Krasnosel'skii's fixed point theorem in cone, we obtain various new results on the existence of positive solution, and the solution is strictly increasing. Finally we give an example. |
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| Keywords: | positive solutions singular third-order three-point BVP fixed point theorem |
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