A semilinear elliptic equation with competing powers and a radial potential

Monica Musso, Juliana Pimentel

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Abstract

We verify the existence of radial positive solutions for the semilinear equation (Formula presented.) where N ≥ 3, p is close to p* ≔ (N+ 2)/(N − 2), and V is a radial smooth potential. If q is super-critical, namely q > p*, we prove that this problem has a radial solution behaving like a superposition of bubbles blowing-up at the origin with different rates of concentration, provided V(0) < 0. On the other hand, if N/(N − 2) < q < p*, we prove that this problem has a radial solution behaving like a super-position of flat bubbles with different rates of concentration, provided lim r→∞V(r) < 0.

Original languageEnglish
Pages (from-to)283-298
Number of pages16
JournalJournal d'Analyse Mathematique
Volume140
Issue number1
DOIs
Publication statusPublished - 1 Mar 2020

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)

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