Brezis-Nirenberg type theorems and multiplicity of positive solutions for a singular elliptic problem

被引：88

作者：

Hirano, Norimichi ^{[2
]}

Saccon, Claudio ^{[1
]}

Shioji, Naoki ^{[2
]}

机构：

[1] Univ Pisa, Dept Appl Math Ulisse Dini, I-56126 Pisa, Italy

[2] Yokohama Natl Univ, Dept Math, Grad Sch Environm & Informat Sci, Yokohama, Kanagawa 2408501, Japan

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2008年 / 245卷 / 08期

基金：

日本学术振兴会;

关键词：

Brezis-Nirenberg type theorems; singular elliptic problem; positive solutions;

D O I：

10.1016/j.jde.2008.06.020

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study Brezis-Nirenberg type theorems for the equation -Delta u + g(x, u) = f(x, u) in Omega. u = 0 on partial derivative Omega, where Omega is a bounded domain in R-N, g(x, .) is increasing and f is a dissipative nonlinearity. We apply such theorems for studying existence and multiplicity of positive solutions for the equation -Delta u = u(-q) + lambda u(p) in Omega, u = 0 on partial derivative Omega, where q > 0, p > 1 and lambda > 0. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：1997 / 2037

页数：41

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