| p-Laplacian算子边值问题在半正无穷区间正解的存在性 |
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| 引用本文： | 廉立芳,葛渭高.p-Laplacian算子边值问题在半正无穷区间正解的存在性[J].北京理工大学学报,2003,23(6):679-681. |
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| 作者姓名： | 廉立芳 葛渭高 |
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| 作者单位： | 北京理工大学,理学院数学系,北京,100081 |
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| 基金项目： | 国家自然科学基金;19871005; |
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| 摘 要： | 讨论有关p-Laplacian算子的边值问题在半正无穷区间正解的存在性．首先讨论有限区间上正解的存在性，把边值问题转化成全连续算子方程．根据不动点定理得出算子方程不动点的存在性，由更替定理相应得到有限区间上p-Laplacian边值问题正解的存在性．再由Arzela—Ascoli定理把有限区间延伸到半正无穷区间，得出无穷区间边值问题正解的存在性。
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| 关 键 词： | p-Laplacian算子 正解的存在 全连续 不动点 |
| 文章编号： | 1001-0645(2003)06-0679-03 |
| 收稿时间： | 2002/11/28 0:00:00 |
| 修稿时间： | 2002年11月28日 |
Existence of Positive Solutions for the p-Laplacian BVPS on the Semi-Infinite Interval |
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| LIAN Li-fang and GE Wei-gao.Existence of Positive Solutions for the p-Laplacian BVPS on the Semi-Infinite Interval[J].Journal of Beijing Institute of Technology(Natural Science Edition),2003,23(6):679-681. |
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| Authors: | LIAN Li-fang and GE Wei-gao |
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| Institution: | Department of Mathematics, School of Science, Beijing Institute of Technology, Beijing100081, China;Department of Mathematics, School of Science, Beijing Institute of Technology, Beijing100081, China |
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| Abstract: | The existence of positive solutions of p -Laplacian boundary value problems is studied on the semi-infinite interval. After studying the existence of positive solutions on the base of fixed point theorem of p -Laplacian operator boundary value problems on the finite interval, the interval can be extended applying the Arzela-Ascoli theorem from the finite to the semi-infinite interval. So the conclusion is found about the existence of positive solutions of p -Laplacian boundary value problems on the semi-infinite interval. |
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| Keywords: | p-Laplacian operator existence of positive solutions completely continuous fixed point |
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