Mathematical Research Letters

Volume 22 (2015)

Number 6

On a fractional Henon equation and applications

Pages: 1791 – 1804

DOI: http://dx.doi.org/10.4310/MRL.2015.v22.n6.a13

Authors

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

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

Abstract

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.

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