Infinitely many positive solutions to some scalar field equations with nonsymmetric coefficients

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Abstract

In this paper the equation -Delta u+a(x)u=|u|^{p-1}u in R^N is considered, when N ge 2, p > 1 and p < N+2/N-2 if N ge 3. Assuming that the potential a(x) is a positive function belonging to L^{N/2}_loc (R^N) such that a(x)to a_infty > 0, as |x|toinfty, and satisfies slow decay assumptions but does not need to fulfill any symmetry property, the existence of infinitely many positive solutions, by purely variational methods, is proved. The shape of the solutions is described as is, and furthermore, their asymptotic behavior when |a(x)-a_infty|_{L^{N/2}_{loc}}to 0.

Autore Pugliese

Tutti gli autori

  • G. Cerami , D. Passaseo , S.Solimini

Titolo volume/Rivista

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS

Anno di pubblicazione

2013

ISSN

0010-3640

ISBN

Non Disponibile

Numero di citazioni Wos

22

Ultimo Aggiornamento Citazioni

28/04/2018

Numero di citazioni Scopus

24

Ultimo Aggiornamento Citazioni

28/04/2018

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile