On the Location of Blow up Points of Least Energy Solutions to the Brezis-Nirenberg Equation

被引：4

作者：

Takahashi, Futoshi ^{[1
]}

机构：

[1] SEG, Shinjuku Ku, Tokyo 1600023, Japan

来源：

FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA | 2004年 / 47卷 / 01期

关键词：

Least energy solutions; Critical Sobolev exponent; Robin function; Blow up point;

D O I：

10.1619/fesi.47.145

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the asymptotic behavior of solutions to the semi-linear elliptic problem involving critical Sobolev exponent with lower order perturbation, which was considered by Han and Rey before. We focus our attention on the least energy solutions obtained by the method of Brezis and Nirenberg, and show that the blow up point of the least energy solutions is a minimum point of the (positive) Robin function on the domain. This additional characterization extends the former result of Han and Rey in this case.

引用

页码：145 / 166

页数：22

共 11 条

[1] 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
[2] MULTIPLE SOLUTIONS OF H-SYSTEMS AND RELLICH CONJECTURE
BREZIS, H
CORON, JM
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1984, 37 (02) : 149 - 187
[3] Brezis H., 1989, PARTIAL DIFFERENTIAL, P149
[4] HAN ZC, 1991, ANN I H POINCARE-AN, V8, P159
[5] Isobe T., 2001, ADV DIFFERENTIAL EQU, V6, P641
[6] Isobe T, 2001, ADV DIFFERENTIAL EQU, V6, P513
[7] THE ROLE OF THE GREENS-FUNCTION IN A NONLINEAR ELLIPTIC EQUATION INVOLVING THE CRITICAL SOBOLEV EXPONENT
REY, O
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1990, 89 (01) : 1 - 52
[8] PROOF OF 2 CONJECTURES OF BREZIS,H, AND PELETIER,L.A.
REY, O
[J]. MANUSCRIPTA MATHEMATICA, 1989, 65 (01) : 19 - 37
[9] STRUWE M, 1984, MATH Z, V187, P511, DOI 10.1007/BF01174186
[10] Asymptotic behavior of least energy solutions to a semilinear Dirichlet problem near the critical exponent
Wei, JC
[J]. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 1998, 50 (01) : 139 - 153

← 1 2 →