关于含临界指数的p-平均曲率算子

数学季刊 ›› 2006, Vol. 21 ›› Issue (4): 511-521.

关于含临界指数的p-平均曲率算子

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

收稿日期:2003-09-20 出版日期:2006-12-30 发布日期:2023-11-20
作者简介:FU Hong-zhuo(1966-),femail,native of Gaoan,Jiangxi,an associate professor of South China University of Technology,Ph.D.,engages in differential equations.
基金资助:
Supported by the National Natural Science Foundation of China(10171032)； Supported by the Guangdong Provincial Natural Science Foundation of China(011606)；

On p-mean Curvature Operator with Critical Exponent

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

Received:2003-09-20 Online:2006-12-30 Published:2023-11-20
About author:FU Hong-zhuo(1966-),femail,native of Gaoan,Jiangxi,an associate professor of South China University of Technology,Ph.D.,engages in differential equations.
Supported by:
Supported by the National Natural Science Foundation of China(10171032)； Supported by the Guangdong Provincial Natural Science Foundation of China(011606)；

摘要/Abstract

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: ... is 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.

关键词: mean curvature operator, critical exponent, (PS)condition, dual set

Abstract: This paper is concerned with the existence of positive solutions of the following Dirichlet problem for p-mean curvature operator with critical exponent: ... is 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.

Key words: mean curvature operator, critical exponent, (PS)condition, dual set

中图分类号:

O175.25

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.

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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