  We consider the following critical semilinear nonlocal equation involving the
fractional Laplacian $$ (-\Delta)^su=K(|x|)|u|^{2^*_s-2}u,\ \ \hbox{in}\ \
\mathbb{R}^N, $$ where $K(|x|)$ is a positive radial function, $N>2+2s$,
$0<s<1$, and $2^*_s=\frac{2N}{N-2s}$. Under some asymptotic assumptions on
$K(x)$ at an extreme point, we show that this problem has infinitely many
non-radial positive or sign-changing solutions.
