Mathematical Research Letters

Volume 22 (2015)

Number 6

On a fractional Henon equation and applications

Pages: 1791 – 1804



Yannick Sire (LATP, UMR CNRS 7353, Université Aix-Marseille, France)

Jun-Cheng Wei (Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada)


We investigate some nonlocal equations in bounded domains for different kinds of operators with power nonlinearities. We prove an existence result in the spirit of an earlier work by W.-M. Ni. As an application, we prove the existence of solutions to nonlocal supercritical equations in the complement of a ball. We prove also some regularity results for higher order nonlocal equations, of independent interest.

Accepted 17 October 2014

Published 23 May 2016