  We analyze existence, multiplicity and oscillatory behavior of positive
radial solutions to a class of quasilinear equations governed by the
Lorentz-Minkowski mean curvature operator. The equation is set in a ball or an
annulus of $\mathbb R^N$, is subject to homogeneous Neumann boundary
conditions, and involves a nonlinear term on which we do not impose any growth
condition at infinity. The main tool that we use is the shooting method for
ODEs.
