Symmetry and symmetry breaking for ground state solutions of some strongly coupled elliptic systems
作者: Denis BonheureEderson Moreira dos SantosMiguel Ramos
作者单位: 1Département de Mathématique, Université Libre de Bruxelles, CP 214, Boulevard du Triomphe, B-1050 Bruxelles, Belgium
2Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668, CEP 13560-970, São Carlos, SP, Brazil
3University of Lisbon, CMAF, Faculty of Science, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal
刊名: Journal of Functional Analysis, 2013, Vol.264 (1), pp.62-96
来源数据库: Elsevier Journal
DOI: 10.1016/j.jfa.2012.10.002
关键词: Hamiltonian elliptic systemsHénon weightsSupercritical problemsSchwarz foliated symmetrySymmetry breakingGround state solution
原始语种摘要: Abstract(#br)We consider the ground state solutions of the Lane–Emden system with Hénon-type weights − Δ u = | x | β | v | q − 1 v , − Δ v = | x | α | u | p − 1 u in the unit ball B of R N with Dirichlet boundary conditions, where N ⩾ 1 , α , β ⩾ 0 , p , q > 0 and 1 / ( p + 1 ) + 1 / ( q + 1 ) > ( N − 2 ) / N . We show that such ground state solutions u , v 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 α , β , p and q under which the ground state solutions are not radially symmetric.
全文获取路径: Elsevier  (合作)
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来源刊物:
影响因子:1.252 (2012)

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关键词翻译
关键词翻译
  • symmetry 对称
  • breaking 破碎
  • elliptic 椭圆形的
  • coupled 耦合
  • state 状态
  • Hamiltonian 哈密(尔)顿
  • respect 珍视
  • foliated 叶片状的
  • weights 法码
  • symmetric 对称的