Existence and symmetry of least energy nodal solutions for Hamiltonian elliptic systems
作者: Denis BonheureEderson Moreira dos SantosMiguel RamosHugo Tavares
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, CP 668, CEP 13560-970, São Carlos, SP, Brazil
3CMAF, Faculty of Science, University of Lisbon, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal
4Center for Mathematical Analysis, Geometry and Dynamical Systems, Mathematics Department — Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
刊名: Journal de mathématiques pures et appliquées, 2015, Vol.104 (6), pp.1075-1107
来源数据库: Elsevier Journal
DOI: 10.1016/j.matpur.2015.07.005
关键词: Hamiltonian elliptic systemsHénon weightsLeast energy nodal solutionsFoliated Schwarz symmetrySymmetry-breaking
原始语种摘要: Abstract(#br)In this paper we prove existence of least energy nodal solutions for the Hamiltonian elliptic system with Hénon-type weights − Δ u = | x | β | v | q − 1 v , − Δ v = | x | α | u | p − 1 u in Ω , u = v = 0 on ∂ Ω , where Ω is a bounded smooth domain in R N , N ≥ 1 , α , β ≥ 0 and the nonlinearities are superlinear and subcritical, namely 1 > 1 p + 1 + 1 q + 1 > N − 2 N . When Ω is either a ball or an annulus centred at the origin and N ≥ 2 , we show that these solutions display the so-called foliated Schwarz symmetry. It is natural to conjecture that these solutions are not radially symmetric. We provide such a symmetry breaking in a range of parameters where the solutions of the system behave like...
全文获取路径: Elsevier  (合作)
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关键词翻译
关键词翻译
  • symmetry 对称
  • elliptic 椭圆形的
  • least 最少的
  • width 幅度
  • Hamiltonian 哈密(尔)顿
  • nodal 部件的
  • article 冠词
  • energy 能量
  • symmetric 对称的
  • existence 存在