Symmetry and symmetry breaking for ground state solutions of some strongly coupled elliptic systems

被引：20

作者：

Bonheure, Denis ^{[2
]}

dos Santos, Ederson Moreira ^{[3
]}

Ramos, Miguel ^{[1
]}

机构：

[1] Univ Lisbon, CMAF, Fac Sci, P-1649003 Lisbon, Portugal

[2] Univ Libre Bruxelles, Dept Math, B-1050 Brussels, Belgium

[3] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP, Brazil

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2013年 / 264卷 / 01期

基金：

巴西圣保罗研究基金会;

关键词：

Hamiltonian elliptic systems; Henon weights; Supercritical problems; Schwarz foliated symmetry; Symmetry breaking; Ground state solution; ASYMPTOTIC-BEHAVIOR; DIRICHLET PROBLEM; HENON EQUATION;

D O I：

10.1016/j.jfa.2012.10.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the ground state solutions of the Lane-Emden system with Henon-type weights -Delta u = vertical bar x vertical bar(beta)vertical bar nu vertical bar(q-1)nu,-Delta u = vertical bar x vertical bar(alpha)vertical bar u vertical bar(p-1) u in the unit ball B of R-N with Dirichlet boundary conditions, where N >= 1, alpha, beta >= 0, p, q > 0 and 1/(p + 1) + 1/(q + 1) > (N - 2)/N. We show that such ground state solutions u, u always have definite sign in B and exhibit a foliated Schwarz symmetry with respect to a unit vector of R-N. We also give precise conditions on the parameters alpha, beta, p and q under which the ground state solutions are not radially symmetric. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：62 / 96

页数：35

共 31 条

[1] Singularly perturbed elliptic systems [J].

Alves, CO ;

Soares, SHM .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 64 (01) :109-129

[2] Partial symmetry of least energy nodal solutions to some variational problems [J].

Bartsch, T ;

Weth, T ;

Willew, M .

JOURNAL D ANALYSE MATHEMATIQUE, 2005, 96 (1) :1-18

[3] Radial symmetry of positive solutions to nonlinear polyharmonic Dirichlet problems [J].

Berchio, Elvise ;

Gazzola, Filippo ;

Weth, Tobias .

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2008, 620 :165-183

[4]

Bonheure D, 2012, T AM MATH SOC, V364, P447

[5] Multiple critical points of perturbed symmetric strongly indefinite functionals [J].

Bonheure, Denis ;

Ramos, Miguel .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2009, 26 (02) :675-688

[6] An approach to symmetrization via polarization [J].

Brock, F ;

Solynin, AY .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 352 (04) :1759-1796

[7] On the Henon equation: asymptotic profile of ground states, I [J].

Byeon, Jaeyoung ;

Wang, Zhi-Qiang .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2006, 23 (06) :803-828

[8] Radial and non radial solutions for Hardy-Henon type elliptic systems [J].

Calanchi, Marta ;

Ruf, Bernhard .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2010, 38 (1-2) :111-133

[9] Asymptotic behavior for elliptic problems with singular coefficient and nearly critical Sobolev growth [J].

Cao, Daomin ;

Peng, Shuangjie .

ANNALI DI MATEMATICA PURA ED APPLICATA, 2006, 185 (02) :189-205

[10]

Clement P., 1996, NONLINEAR EVOLUTION, P132

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