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...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.展开更多
基金National Natural Science Foundation of China（10171032） and the Guangdong Provincial Natural Science Foundation of China（011606）
文摘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.
