Multiplicity of ground states for the scalar curvature equation

Francesca Dalbono, Andrea Sfecci, Matteo Franca

Risultato della ricerca: Article

2 Citazioni (Scopus)

Abstract

We study existence and multiplicity of radial ground states for the scalar curvature equation Δu+K(|x|)un+2n-2=0,x∈Rn,n>2,when the function K: R+→ R+ is bounded above and below by two positive constants, i.e. 0 0 , it is decreasing in (0, 1) and increasing in (1 , + ∞). Chen and Lin (Commun Partial Differ Equ 24:785–799, 1999) had shown the existence of a large number of bubble tower solutions if K is a sufficiently small perturbation of a positive constant. Our main purpose is to improve such a result by considering a non-perturbative situation: we are able to prove multiplicity assuming that the ratio K¯/K̲ is smaller than some computable values.
Lingua originaleEnglish
pagine (da-a)273-298
Numero di pagine26
RivistaAnnali di Matematica Pura ed Applicata
Volume199
Stato di pubblicazionePublished - 2020

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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