  In this paper, we consider the semilinear equation involving the fractional
Laplacian in the Euclidian space $\mathbb{R}^n$: \begin{equation}
(-\Delta)^{\alpha/2} u(x) = f(x_n) \,u^p(x), \quad x \in \mathbb{R}^n
\label{n26} \end{equation} in the subcritical case with
$1<p<\frac{n+\alpha}{n-\alpha}$. Instead of carrying out direct investigations
on pseudo-differential equation (\ref{n26}), we first seek its equivalent form
in an integral equation as below: \begin{equation}
u(x)=\int_{\mathbb{R}^n}G_{\infty}(x,y)\,f(y_n)\, u^{p}(y)\,dy, \label{n27}
\end{equation} where $ G_{\infty}(x,y)$ is the Green's function associated with
the fractional Laplacian in $\mathbb{R}^n$. Exploiting the \emph{method of
moving planes in integral forms}, we are able to derive the nonexistence of
positive solutions for (\ref{n27}) in the subcritical case. Hence the same
conclusion is true for (\ref{n26}).
