Infinitely many positive solutions for a nonlinear field equation with super-critical growth

Monica Musso; Juncheng Wei; Shusen Yan

doi:10.1112/plms/pdv063

Infinitely many positive solutions for a nonlinear field equation with super-critical growth

Monica Musso, Juncheng Wei, Shusen Yan

Mathematics

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

We consider the following nonlinear field equation with super-critical growth: (∗) −Δu + λu = Q(y)u(N+2)/(N−2), u>0 inRN+m, u(y) →0 as |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).

Original language	English
Pages (from-to)	1-26
Journal	Proceedings of the London Mathematical Society
Volume	112
Issue number	1
DOIs	https://doi.org/10.1112/plms/pdv063
Publication status	Published - 2016

Keywords

Partial Differential Equations

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10.1112/plms/pdv063

https://hdl.handle.net/1959.11/20208

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title = "Infinitely many positive solutions for a nonlinear field equation with super-critical growth",

abstract = "We consider the following nonlinear field equation with super-critical growth: (∗) −Δu + λu = Q(y)u(N+2)/(N−2), u>0 inRN+m, u(y) →0 as |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).",

keywords = "Partial Differential Equations",

author = "Monica Musso and Juncheng Wei and Shusen Yan",

year = "2016",

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AU - Musso, Monica

AU - Wei, Juncheng

AU - Yan, Shusen

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N2 - We consider the following nonlinear field equation with super-critical growth: (∗) −Δu + λu = Q(y)u(N+2)/(N−2), u>0 inRN+m, u(y) →0 as |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).

AB - We consider the following nonlinear field equation with super-critical growth: (∗) −Δu + λu = Q(y)u(N+2)/(N−2), u>0 inRN+m, u(y) →0 as |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).

KW - Partial Differential Equations

UR - https://www.scopus.com/pages/publications/84959917158

U2 - 10.1112/plms/pdv063

DO - 10.1112/plms/pdv063

M3 - Article

SN - 0024-6115

VL - 112

SP - 1

EP - 26

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

IS - 1

ER -

Infinitely many positive solutions for a nonlinear field equation with super-critical growth

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