| 奇异临界椭圆问题的正解 |
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| 引用本文： | 公艳.奇异临界椭圆问题的正解[J].吉首大学学报(自然科学版),2005,26(2):83-86. |
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| 作者姓名： | 公艳 |
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| 作者单位： | (浙江师范大学数理学院，浙江 金华 321004) |
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| 摘 要： | 考虑奇异方程-Δpu=｜u｜r-2u+（｜u｜p(s)-2u）/（｜x｜s）+f(x,u)解的存在性,研究了其所对应的变分泛函的(P.S.)序列,给出了一个局部紧性结果,选择特殊的山路定理和能量估计,证明了方程所对应的变分泛函满足局部的(P.S.)条件时,则存在一个山路型的临界点.
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| 关 键 词： | 奇异 变分方法 Sobolev嵌入 Hardy不等式 |
| 文章编号： | 1007-2985（2005）02-0083-04 |
| 收稿时间： | 2004-11-12 |
| 修稿时间： | 2004-11-12 |
Positive solutions for Singular Critical Elliptic Problems |
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| GONG Yan.Positive solutions for Singular Critical Elliptic Problems[J].Journal of Jishou University(Natural Science Edition),2005,26(2):83-86. |
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| Authors: | GONG Yan |
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| Institution: | (Department of Mathematics,Zhejiang Normal University,Jinhua 321004,Zhejiang China) |
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| Abstract: | The author deals with the conditions of the existence of the singular elliptic equation -Δpu=｜u｜r-2u+( ｜u｜p(s)-2u）/（｜x｜s）+ f(x,u). An analysis on the (P.S.) sequence of the variational functionals corresponding to the equations is given and a local compactness result is obtained.By choosing special Mountain Pass theorem and energy estimate,the author obtains that if the variational functionals corresponding to the equations satisfy local (P.S.) condition,there exsits a critical point,then the author proves the exitence of positive solutions. |
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| Keywords: | singularity variational method sobolev embedding hardy inequality |
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