  This paper is concerned with the elliptic problem for a scalar field equation
with a forcing term \begin{equation} \tag{P}-\Delta u+u=u^p+ \kappa \mu \quad
\mbox{in} \quad{\bf R}^N, \quad u>0 \quad \mbox{in} \quad {\bf R}^N, \quad
u(x)\to 0\quad \mbox{as} \quad |x| \to \infty, \end{equation} where $N\ge 2$,
$p>1$, $\kappa>0$ and $\mu$ is a Radon measure in ${\bf R}^N$ with a compact
support. Under a suitable integrability condition on $\mu$, we give a complete
classification of the solvability of problem~(P) with $1<p<p_{JL}$. Here
$p_{JL}$ is the Joseph-Lundgren exponent defined by $$
  p_{JL} :=\infty\quad\mbox{if}\quad N\le 10,
  \qquad p_{JL}:=\frac{(N-2)^2-4N+8\sqrt{N-1}}{(N-2)(N-10)}\quad \text{if}
\quad N\ge 11. $$
