| 一类Dirichlet问题正解的精确个数 |
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| 引用本文： | 沈柳平,杨继昌.一类Dirichlet问题正解的精确个数[J].黄冈师范学院学报,2010,30(6):32-35. |
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| 作者姓名： | 沈柳平 杨继昌 |
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| 作者单位： | 柳州师范高等专科学校数学与计算机科学系,广西柳州545004 |
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| 摘 要： | 研究Dirichlet问题-=λ（u~p＋u~q）,u（0）=u（1）=0,其中1〈p〈q〈＋∞,参数λ〉0,得到了在1〈p〈q〈p＋1条件下,存在λ＊〉0,当λ≤λ＊时,此方程无正解;当λ〉λ＊时,此方程恰好有一个正解.
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| 关 键 词： | 广义平均曲率方程 正解 精确个数 |
Exact number of positive solutions to a class of Dirichlet problems |
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| SHEN Liu-ping,YANG Ji-chang.Exact number of positive solutions to a class of Dirichlet problems[J].Journal of Huanggang Normal University,2010,30(6):32-35. |
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| Authors: | SHEN Liu-ping YANG Ji-chang |
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| Institution: | (Department of Mathematics and Computer Science,Liuzhou Teachere College,Liuzhou 545004,Cuangxi,China) |
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| Abstract: | We Study the exact number of positive solutions to the problem for the one-dimensional prescribed mean curvature equation -（u＇/（1＋u＇2）（1/2））＇=λ（u~p＋u~q）,u（0）=u（1）=0,with 1pqp ＋1.We find aλ＊0,so that ifλ≤λ＊,this problem has no positive solution,and ifλλ＊,then this problem has one positive solution. |
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| Keywords: | precribed mean curvature equation positive solution exact number |
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