Vol. 271, No. 1, 2014

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ISSN: 0030-8730
Perturbations of a critical fractional equation

Eduardo Colorado, Arturo de Pablo and Urko Sánchez

Vol. 271 (2014), No. 1, 65–85
Abstract

We deal with the following fractional critical problem:

(Δ)α2u = |u|2α(Nα)u + f(x) in Ω, u = 0  on Ω,

where Ω N is a regular bounded domain, 0 < α < 2 and N > α. Under appropriate conditions on the size of f, we prove existence and multiplicity of solutions.

Keywords
semilinear elliptic equations, fractional Laplacian, critical problem
Mathematical Subject Classification 2010
Primary: 35A15, 49J35, 35R11
Milestones
Received: 11 April 2013
Revised: 8 July 2013
Accepted: 12 July 2013
Published: 10 September 2014
Authors
Eduardo Colorado
Departamento de Matemáticas
Universidad Carlos III de Madrid
Avenida Universidad 30
28911 Leganés
Spain
Instituto de Ciencias Matemáticas, ICMAT (CSIC-UAM-UC3M-UCM)
C/ Nicolás Cabrera 15
28049 Madrid
Spain.
Arturo de Pablo
Departamento de Matemáticas
Universidad Carlos III de Madrid
Avenida Universidad 30
28911 Leganés
Spain
Urko Sánchez
Universidad Carlos III de Madrid
28911 Leganés
Spain