Asymptotic behavior of the least energy solution of a problem with competing powers

被引：8

作者：

Dancer, E. N. ^{[1
]}

Santra, Sanjiban ^{[1
]}

Wei, Juncheng ^{[2
]}

机构：

[1] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia

[2] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2011年 / 261卷 / 08期

基金：

澳大利亚研究理事会;

关键词：

Least energy solution; Asymptotic behavior; Zero mass; SEMILINEAR ELLIPTIC-EQUATIONS; POSITIVE SOLUTIONS; SUPERCRITICAL GROWTH; SINGULAR SOLUTIONS; SYMMETRY; LOCATION;

D O I：

10.1016/j.jfa.2011.06.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the problem epsilon(2)Delta u - u(q) + u(P) = 0 in Omega, u > 0 in Omega, u = 0 on partial derivative Omega. Here Omega is a smooth bounded domain in R(N), 1 < q < p < N+2/N-2 if N >= 3 and epsilon is a small positive parameter. We study the asymptotic behavior of the least energy solution as e goes to zero in the case q <= N/N-2. We show that the limiting behavior is dominated by the singular solution Delta G - G(q) = 0 in Omega\{P}, G = 0 on partial derivative Omega. The reduced energy is of nonlocal type. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：2094 / 2134

页数：41

共 25 条

[1]

BERESTYCKI H, 1983, ARCH RATION MECH AN, V82, P313

[2]

Bethuel F., 1994, Progress in Nonlinear Differential Equations and Their Applications, V13

[3]

BREZIS H, 1980, ARCH RATION MECH AN, V75, P1

[4]

BREZIS H, 1987, ARCH RATION MECH AN, V99, P249

[5] Singular perturbed problems in the zero mass case: asymptotic behavior of spikes [J].

Dancer, E. N. ;

Santra, Sanjiban .

ANNALI DI MATEMATICA PURA ED APPLICATA, 2010, 189 (02) :185-225

[6] SOME NOTES ON THE METHOD OF MOVING PLANES [J].

DANCER, EN .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1992, 46 (03) :425-434

[7] Two-bubble solutions in the super-critical Bahri-Coron's problem [J].

del Pino, M ;

Felmer, P ;

Musso, M .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2003, 16 (02) :113-145

[8]

del Pino M, 1999, INDIANA U MATH J, V48, P883

[9] Singular limits in Liouville-type equations [J].

del Pino, M ;

Kowalczyk, M ;

Musso, M .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2005, 24 (01) :47-81

[10] Variational reduction for Ginzburg-Landau vortices [J].

del Pino, Manuel ;

Kowalczyk, Michal ;

Musso, Monica .

JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 239 (02) :497-541

← 1 2 3 →