南京师大学报（自然科学版）2008，Vol.31Issue(4)：1-7,7.
带非齐次项和Sobolev-Hardy临界指数的奇异椭圆方程的多解
Multiple Solutions for Elliptic Equation With Critical Sobolev-Hardy Exponent and Inhomogeneous Term
摘要
Abstract
Let 2*=2(N+α)/(N-2+β), N≥3 be the limiting Sobolev exponent and Ω(∪)RN open bounded set. It is showed that for f(χ)∈H-1β satisfying a suitable condition and f(χ)≠0, the weighed elliptic problem:{-div(|χ|β▽u)=|χ|αup*-1+εf(x),χ∈Ω,u>0,x∈Ω,u=0,χ∈(e)Ω,admits two solutions u- and in H1, p0,β(Ω). Also u-≥0 and ≥0 for f(χ)≥0. Notice that, in general, this is not the case if f(χ)=0.关键词
p-阶拉普拉斯方程/临界指数/最佳常数/Sobolev-Hardy不等式Key words
p-Laplace equation,critical exponent,best constant,Sobolev-Hardy inequality分类
数理科学引用本文复制引用
穆罕麦德,沈尧天,姚仰新..带非齐次项和Sobolev-Hardy临界指数的奇异椭圆方程的多解[J].南京师大学报（自然科学版）,2008,31(4):1-7,7.基金项目
Supported by the National Science Foundation of China (10771074). （10771074）
