Quasilinear Elliptic Equations with Neumann Boundary and Singularity  

作　　者：Bing-yu Kou Shuang-jie Peng 

机构地区：[1]School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China [2]Institute of Science, PLA University of Science and Technology, Nanjing, 210007, China

出　　处：《Acta Mathematicae Applicatae Sinica》2009年第4期631-646,共16页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.10631030);the Program for New Century Excellent Talents in University(No.07-0350);the Key Project of Chinese Ministry of Education(No.107081)

摘　　要：Let Ω be a bounded domain with a smooth C2 boundary in RN（N ≥ 3）, 0 ∈Ω, and n denote the unit outward normal to ЭΩ.We are concerned with the Neumann boundary problems： -div（｜x｜α｜△u｜p-2△u）=｜x｜βup（α,β）-1-λ｜x｜γup-1,u（x）〉0,x∈Ω,Эu/Эn=0 on ЭΩ,where 1〈p〈N and α〈0,β〈0 such that p（α,β）△=p（N＋β）/N-p＋α〉p,y〉α-p.For various parameters α,βorγ,we establish certain existence results of the solutions in the case 0∈Ω or 0∈ЭΩ.Let Ω be a bounded domain with a smooth C2 boundary in RN（N ≥ 3）, 0 ∈Ω, and n denote the unit outward normal to ЭΩ.We are concerned with the Neumann boundary problems： -div（｜x｜α｜△u｜p-2△u）=｜x｜βup（α,β）-1-λ｜x｜γup-1,u（x）〉0,x∈Ω,Эu/Эn=0 on ЭΩ,where 1〈p〈N and α〈0,β〈0 such that p（α,β）△=p（N＋β）/N-p＋α〉p,y〉α-p.For various parameters α,βorγ,we establish certain existence results of the solutions in the case 0∈Ω or 0∈ЭΩ.

关 键 词：Singular equations Caffarelli-Kohn-Nirenberg inequalities critical exponents ground state sloutions 

分 类 号：O29[理学—应用数学]