Existence of Positive Solutions for a Singular p-Laplacian Differential Equation

作     者：Xia LI Zheng An YAO Wen Shu ZHOU 

作者机构：Department of Mathematics Shenzhen University Shenzhen 518060 P. R. China Department of Mathematics Zhongshan University Guangzhou 510275 P. R. China Department of Mathematics Jilin University Changchun 130012 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2008年第24卷第8期

页      面：1331-1344页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Natural Science Foundation of China 2004 (NNSFC-10171113 and NNSFC-10471156) Tianyuan Youth Foundation (No.10626056) Natural Science Foundation of GuangDong 2004 (NSFGD4009793) 

主　　题：p-Laplacian differential equation positive solution existence 

摘      要：In this paper, we are concerned with the existence of positive solutions for a singular p-Laplacian differential equation （φp（u＇））＇＋β/r φp（u＇）-γ ｜u＇｜^p/u ＋ g（r）=0,0〈r〈1, subject to the Dirichlet boundary conditions： u（0） = u（1） =0, where φp（s） = ｜sl^P-2s,p 〉 2,β 〉0, γ〉（p-1）/p （β ＋ 1）, and g（r） ∈ C^1 [0, 1] with g（r） 〉 0 for all τ ∈ [0, 1]. We use the method of elliptic regularization, by carrying out two limit processes, to get a positive solution.