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Infinitely many positive solutions for a nonlinear field equation with super‐critical growth
Author(s) -
Musso Monica,
Wei Juncheng,
Yan Shusen
Publication year - 2016
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdv063
Subject(s) - mathematics , bounded function , nonlinear system , mathematical physics , field (mathematics) , symmetry (geometry) , function (biology) , mathematical analysis , pure mathematics , physics , quantum mechanics , geometry , evolutionary biology , biology
We consider the following nonlinear field equation with super‐critical growth:( * )− Δ u + λ u = Q ( y ) u ( N + 2 ) / ( N − 2 ), u > 0inR N + m ,u ( y ) → 0as | y | → + ∞ ,where m ⩾ 1 , λ ⩾ 0 and Q ( y ) is a bounded positive function. We show that equation (*) has infinitely many positive solutions under certain symmetry conditions on Q ( y ) .