Sign-changing solutions at the almost Hénon critical exponent

Research output: Contribution to journalArticle

Abstract

© 2018 Elsevier Inc. We study the problem (Pα)−Δu=|x|α|u|[Formula presented]−εu in Ω,u=0 on ∂Ω where Ω is a bounded smooth domain in RN, N≥3, which is symmetric with respect to x1,x2,…,xNand contains the origin, α>0, and ε>0 is a small parameter. We construct solutions to (Pα) with the shape of a sign-changing tower of bubbles of order α that concentrate and blow-up at the origin as ε→0. We also study a slightly Hénon supercritical dual version of (Pα) in an exterior domain, for which we found solutions with the shape of a flat sign-changing tower of bubbles of order α that disappear as ε→0.
Original languageEnglish
Pages (from-to)624-642
Number of pages19
JournalJournal of Mathematical Analysis and Applications
DOIs
Publication statusPublished - 1 Sep 2018

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