| 一维p-拉普拉斯三个正解的存在性 |
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| 引用本文： | 白占兵,葛渭高. 一维p-拉普拉斯三个正解的存在性[J]. 数学学报, 2006, 49(5): 1045-105. DOI: cnki:ISSN:0583-1431.0.2006-05-012 |
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| 作者姓名： | 白占兵 葛渭高 |
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| 作者单位： | [1]山东科技大学信息科学与工程学院,青岛266510 [2]北京理工大学应用数学系,北京100081 |
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| 基金项目： | 国家自然科学基金资助项目（10371006） |
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| 摘 要： | 考虑边值问题:(p(x'(t)))'+q(t)f(t,x(t),x'(t))=0,P>1,t∈[0,1],边值条件为x(0)=x(1)=0或x(0)=x'(1)=0．借助于一个新的不动点定理我们获得了存在至少三个正解的充分条件．问题的关键是非线性项f依赖于未知函数的一阶导数．最后,给出一个具体的例子．
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| 关 键 词： | p-拉普拉斯 边值问题 不动点定理 |
| 文章编号： | 0583-1431（2006）05-1045-08 |
| 收稿时间： | 2004-06-01 |
| 修稿时间： | 2004-06-012005-07-30 |
Existence of Three Positive Solutions for the One-Dunensional p-Laplacian |
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| Zhan Bing BAI, Wei Gao GE. Existence of Three Positive Solutions for the One-Dunensional p-Laplacian[J]. Acta Mathematica Sinica, 2006, 49(5): 1045-105. DOI: cnki:ISSN:0583-1431.0.2006-05-012 |
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| Authors: | Zhan Bing BAI Wei Gao GE |
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| Affiliation: | College of Inforraation Science and Technology, Shandong University of Science and Technology;Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, P. R. China |
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| Abstract: | We consider the boundary value problem:((?)p(x'(t)))'+q(t)f(t,x(t),x'(t))=0,P>1,t∈[0,1],with x(0)=x(1)=0 or x(0)=x'(1)=0. By using a new fixed point theorem, sufficient conditions are obtained that guarantee the existence of at least three positive solutions. The key point here is that the nonlinear term f is dependent on the first order derivative. An example is that also included to illustrate the importance of the results obtained. |
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| Keywords: | p-Laplacian boundary value problem fixed-point theorem |
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