#### Vol. 271, No. 1, 2014

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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:

where $\Omega \subset {ℝ}^{N}$ is a regular bounded domain, $0<\alpha <2$ and $N>\alpha$. 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