THE EXISTENCES OF POSITIVE SOLUTIONS FOR P-MEAN CURVATURE OPERATOR WITH SUPERCRITICAL POTENTIAL  

作　　者：Fu Hongzhuo Shen Yaotian 

机构地区：[1]School of Mathematical Siences, South China University of Technology, Guangzhou, 510640 [2]Department of Mathematics, University of Science and Technology of China, Hefei, 230026, China [3]School of Mathematical Siences, South China University of Technology, Guangzhou, 510640, China

出　　处：《Journal of Partial Differential Equations》2005年第3期193-205,共13页偏微分方程（英文版）

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

摘　　要：This paper is concerned with the existences of positive solutions of the following Dirichlet problem for p-mean curvature operator with supercritical potential：{-div（（1＋｜ u｜^2）p-2/2 u）=λu^r-1＋μ（u^1q-1,｜x｜^s）,u〉0 x∈Ω,u=0 x∈ЭΩ where u∈ W0^1,P（Ω）,Ω is a bounded domain in R^N（N 〉 p 〉 1） with smooth boundary ЭΩ and 0∈Ω,0 〈 q 〈p, 0≤s〈 N/p（p-q）＋q, p≤r〈p＊, p＊ = Np/N-p,μ〉0. It reaches the conclusion where this problem has two positive solutions in the different cases. It discusses the existences of positive solutions of the Dirichlet problem for the p-mean curvature operator with supercritical potential firstly. Meanwhile, it extends some results of the p-Laplace operator to that of p-mean curvature operator for p ≥2.

关 键 词：Mean curvature operator Mountain Pass Principie （PS） condition Ekeland＇s variational principle. 

分 类 号：O175[理学—数学]