| 关于含临界指数的p-平均曲率算子 |
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| 引用本文： | 傅红卓,沈尧天,杨俊.关于含临界指数的p-平均曲率算子[J].数学季刊,2006,21(4):511-521. |
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| 作者姓名： | 傅红卓 沈尧天 杨俊 |
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| 作者单位： | School of Mathematical Sciences South China University of Technology，School of Mathematical Sciences，South China University of Technology，School of Mathematical Sciences，South China University of Technology，Guangzhou 510640，China Department of Mathematics，University of Science and Technology of China Hefei 230026，China，Guangzhou 510640，China，Guangzhou 510640，China |
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| 基金项目： | Supported by the National Natural Science Foundation of China(10171032)，Supported by the Guangdong Provincial Natural Science Foundation of China(011606) |
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| 摘 要： | This paper is concerned with the existence of positive solutions of the following Dirichlet problem for p-mean curvature operator with critical exponent: -div((1 |▽u|~2)(p-2)/2▽u)=λu~(p*-1) μu~(q-1),u＞0,x∈Ω, u=0,x∈■Ω, where u∈W_0~(1,p)(Ω),Ωis a bounded domain in R~N(N＞p＞1)with smooth boundary ■Ω,2＜=p＜=q＜=P~*,P~*=(Np)/(N-p),λ,P＞0.It reaches the conclusions that this problem has at least one positive solution in the different cases.It is discussed the existences of positive solutions of the Dirichlet problem for the p-mean curvature operator with critical exponent by using Nehari-type duality property firstly.As p=2,q=p,the result is correspond to that of Laplace operator.
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| 关 键 词： | 曲率算子 临界指数 平滑边界 数学分析 |
On p-mean Curvature Operator with Critical Exponent |
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| FU Hong-zhuo,SHEN Yao-tian,YANG Jun.On p-mean Curvature Operator with Critical Exponent[J].Chinese Quarterly Journal of Mathematics,2006,21(4):511-521. |
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| Authors: | FU Hong-zhuo SHEN Yao-tian YANG Jun |
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| Affiliation: | [1]School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, China [2]Department of Mathematics, University of Science and Technology of China, Hefei 230026, China |
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| Abstract: | |
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| Keywords: | mean curvature operator critical exponent (PS)condition dual set |
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