| p-Laplace方程Neumann边值问题的可解性 |
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| 引用本文： | 胡志刚,刘文斌,郑春华.p-Laplace方程Neumann边值问题的可解性[J].大学数学,2007,23(5):105-108. |
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| 作者姓名： | 胡志刚 刘文斌 郑春华 |
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| 作者单位： | 中国矿业大学,理学院,徐州,221008 |
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| 基金项目： | 中国矿业大学科研基金(OK4066)，中国矿业大学青年科学基金(OK4481) |
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| 摘 要： | 主要讨论了一维p-Laplace方程(φp(u′))′=f(t,u,u′),t∈(0,1))在Neumann边值条件u′(0)=0,u′(1)=0下边值问题解的存在性,其中φp(s)=|s|p-2s,s≠0.文中通过使用Leray-Schauder度原理,在适当的条件下,建立了对于p-Laplace方程在共振情形下Neumann边值问题解的存在性的充分条件.
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| 关 键 词： | p-Laplace方程 Neumann边值 度理论 |
| 文章编号： | 1672-1454（2007）05-0105-04 |
| 修稿时间： | 2005-12-31 |
The Existence of Solutions for p-Laplace Equations Subject to Neumann Boundary Value Problem |
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| HU Zhi-gang,LIU Wen-bin,ZHENG Chun-hua.The Existence of Solutions for p-Laplace Equations Subject to Neumann Boundary Value Problem[J].College Mathematics,2007,23(5):105-108. |
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| Authors: | HU Zhi-gang LIU Wen-bin ZHENG Chun-hua |
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| Institution: | School of Science, China University of Mining and Technology, Xuzhou 221008, China |
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| Abstract: | We discuss the existence of solutions for one dimensional p-Laplace equation(φp(u′))′=f(t,u,u′),t∈(0,1)) subject to Neumann boundary value problem at u′(0)=0,u′(1)=0,where φp(s)=|s|p-2s,s≠0.By using the Leray-Schauder degree theory,the sufficient conditions of the existence of solutions for p-Laplace equation subject to Neumann boundary value problem at resonance and at non-resonance are established. |
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| Keywords: | p-Laplace Neumann boundary value degree theory |
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