On p-mean Curvature Operator with Critical Exponent  

作　　者：FU Hong-zhuo SHEN Yao-tian YANG Jun 

机构地区：[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

出　　处：《Chinese Quarterly Journal of Mathematics》2006年第4期511-521,共11页数学季刊（英文版）

基　　金：Supported by the National Natural Science Foundation of China（10171032）; Supported by the Guangdong Provincial Natural Science Foundation of China（011606）

摘　　要：This paper is concerned with the existence of positive solutions of the followingDirichlet problem for p-mean curvature operator with critical exponent： -div（（1 ＋｜↓△u｜^2 ）p-2/2 ↓△u） = λup-1＋μ u=q-1,u 〉 0,x x∈Ω,u=0,x∈ δΩ,where u ∈ W01,P is a bounded domain in R^N（N 〉 p 〉 1） with smooth boundary δΩ, 2≤p ≤q〈p,p=Np/N-p,λ,μ〉0. It reaches the conclusions that this problem has at least one positive solution in the different cases. It is discussed the existences of positivesolutions of the Dirichlet problem for the p-mean curvature operator with critical exponentby using Nehari-type duality property firstly. As p = 2, q = p, the result is correspond tothat of Laplace operator.

关 键 词：mean curvature operator critical exponent （PS） condition dual set 

分 类 号：O177[理学—数学]