ON THE BREZIS-NIRENBERG PROBLEM IN A BALL

被引：0

作者：

Chen, Zhijie ^{[1
]}

Zou, Wenming ^{[1
]}

机构：

[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

来源：

DIFFERENTIAL AND INTEGRAL EQUATIONS | 2012年 / 25卷 / 5-6期

关键词：

LINEAR ELLIPTIC-EQUATIONS; MULTIPLE SOLUTIONS; POSITIVE SOLUTIONS; UNIQUENESS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the following Brezis-Nirenberg type critical exponent problem: {-Delta u = lambda u(q) + u(2)*(-1) in B-R, u > 0 in B-R, u = 0 on partial derivative B-R, where B-R is a ball with radius R in R-N (N >= 3), lambda > 0, 1 <= q < 2* - 1, and 2* is the critical Sobolev exponent. We prove the uniqueness results of the least-energy solution when 3 <= N <= 5 and 1 <= q < 2* - 1. We give extremely accurate energy estimates of the least-energy solutions as R -> 0 for N >= 4 and q = 1.

引用

页码：527 / 542

页数：16

共 21 条

[1] [Anonymous], 1996, VARIATIONAL METHODS, DOI DOI 10.1007/978-3-662-03212-1
[2] NODAL SOLUTIONS OF ELLIPTIC-EQUATIONS WITH CRITICAL SOBOLEV EXPONENTS
ATKINSON, FV
BREZIS, H
PELETIER, LA
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1990, 85 (01) : 151 - 170
[3] EMDEN-FOWLER EQUATIONS INVOLVING CRITICAL EXPONENTS
ATKINSON, FV
PELETIER, LA
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1986, 10 (08) : 755 - 776
[4] Aubin T., 1976, J. Diff. Geom., V11, P573
[5] POSITIVE SOLUTIONS OF NON-LINEAR ELLIPTIC-EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS
BREZIS, H
NIRENBERG, L
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1983, 36 (04) : 437 - 477
[6] AN EXISTENCE RESULT FOR NONLINEAR ELLIPTIC PROBLEMS INVOLVING CRITICAL SOBOLEV EXPONENT
CAPOZZI, A
FORTUNATO, D
PALMIERI, G
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1985, 2 (06): : 463 - 470
[7] CERAMI G, 1984, ANN I H POINCARE-AN, V1, P341
[8] SOME EXISTENCE RESULTS FOR SUPERLINEAR ELLIPTIC BOUNDARY-VALUE-PROBLEMS INVOLVING CRITICAL EXPONENTS
CERAMI, G
SOLIMINI, S
STRUWE, M
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1986, 69 (03) : 289 - 306
[9] Chen Z, 2011, ADV DIFFERENTIAL EQU, V16, P775
[10] Chen Z., NONLINEAR D IN PRESS

← 1 2 3 →