A semilinear elliptic equation with competing powers and a radial potential

Monica Musso, Juliana Pimentel

Research output: Contribution to journalArticle

47 Downloads (Pure)

Abstract

We verify the existence of radial positive solutions for the semi-linear equation −∆u = upV(y)uq, u >0, in RN 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 super-position 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 limr→∞V(r) < 0.
Original languageEnglish
Pages (from-to)283-298
JournalJournal d'Analyse Mathematique
Volume140
Issue number1
DOIs
Publication statusPublished - 1 Mar 2020

    Fingerprint

Cite this