We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation
$$
\begin{cases}
\displaystyle
-\text{div}\bigg(\frac{\nabla v}{\sqrt{1-|\nabla v|^2}}\bigg)=f(|x|,v) & \text{in } B_R,\\v=0 & \text{on } \partial B_R,
\end{cases}
$$
where $B_R$ is a ball in $\mathbb{R}^N$ ($N\ge 2$). According to the behaviour of $f=f(r,s)$ near $s=0$, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.
