We are concerned with a nonnegative solution to the scalar field equation
$$\Delta u + f(u) = 0{\rm in }{\open R}^N,\quad \mathop {\lim }\limits_{|x|\to \infty } u(x) = 0.$$
A classical existence result by Berestycki and Lions [3] considers only the case when
f is continuous. In this paper, we are interested in the existence of a solution when
f is singular. For a singular nonlinearity
f, Gazzola, Serrin and Tang [8] proved an existence result when
$f \in L^1_{loc}(\mathbb {R}) \cap \mathrm {Lip}_{loc}(0,\infty )$ with
$\int _0^u f(s)\,{\rm d}s < 0$ for small
$u>0.$ Since they use a shooting argument for their proof, they require the property that
$f \in \mathrm {Lip}_{loc}(0,\infty ).$ In this paper, using a purely variational method, we extend the previous existence results for
$f \in L^1_{loc}(\mathbb {R}) \cap C(0,\infty )$. We show that a solution obtained through minimization has the least energy among all radially symmetric weak solutions. Moreover, we describe a general condition under which a least energy solution has compact support.