On the Brezis-Nirenberg Problem

被引：56
|
作者：
Schechter, M. [1 ]
Zou, Wenming [2 ]
机构：
[1] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA
[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
来源：
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2010年 / 197卷 / 01期
关键词：
NONLINEAR ELLIPTIC PROBLEMS; CRITICAL SOBOLEV EXPONENTS; SIGN CHANGING SOLUTIONS; MIN-MAX THEOREMS; MORSE INDEX; NODAL SOLUTIONS; CRITICAL-POINTS; EQUATIONS; EXISTENCE; LINKING;
D O I：
10.1007/s00205-009-0288-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the following Brezis-Nirenberg problem (Comm Pure Appl Math 36: 437-477, 1983): -Delta u = lambda u + |u|(2)*(- 2)u, u is an element of H(0)(1) (Omega), where Omega is a bounded smooth domain of R(N) (N >= 7) and 2* is the critical Sobolev exponent. We show that, for each fixed lambda > 0, this problem has infinitely many sign-changing solutions. In particular, if lambda >= lambda(1), the Brezis-Nirenberg problem has and only has infinitely many sign-changing solutions except zero. The main tool is the estimates of Morse indices of nodal solutions.
引用
收藏
页码：337 / 356
页数：20
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