Infinitely many positive solutions for a nonlinear field equation with super‐critical growth | Zendy

Musso Monica | Zendy; Wei Juncheng | Zendy; Yan Shusen | Zendy

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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 ) .

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