The sharp exponent in the study of the nonlocal Hénon equation in ${\mathbb{R}}^n$. A Liouville theorem and an existence result

B. Barrios, A. Quaas

We will consider the nonlocal Hénon equation $$(-\Delta {)}^{s}u=|x{|}^{\alpha }{u}^p,{\mathbb{R}}^N,$$ where $(-\Delta {)}^s$ is the fractional Laplacian operator with $0<s<1$, $-2s<\alpha$, $p>1$ and $N…