A critical Kirchhoff type problem involving a nonlocal operator

Alessio Fiscella, Enrico Valdinoci

Research output: Contribution to journalArticle

184 Citations (Scopus)

Abstract

In this paper we show the existence of non-negative solutions for a Kirchhoff type problem driven by a nonlocal integrodifferential operator, that is -M(∥-u∥-Z2) LKu=λf(x,u)+| u|2*-2u in Ω,u=0in Rn\-Ω where L K is an integrodifferential operator with kernel K, Ω is a bounded subset of Rn, M and f are continuous functions, ∥̇ ∥Z is a functional norm and 2* is a fractional Sobolev exponent.

Original languageEnglish
Pages (from-to)156-170
Number of pages15
JournalNonlinear Analysis, Theory, Methods and Applications
Volume94
DOIs
Publication statusPublished - 1 Jan 2014
Externally publishedYes

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