We discuss existence and multiplicity of solutions of the
one-dimensional autonomous prescribed curvature problem
$$
-\left(
{u'}/{\sqrt{1+{u'}^2}}\right)' = f(u),
\quad
u(0)=0,\,\,u(1)=0,
$$
depending on the behaviour at the origin and at infinity of the
function $f$. We consider solutions that are possibly discontinuous
at the points where they attain the value zero.
