  We are interested in providing new results on a prescribed mean curvature
equation in Lorentz-Minkowski space set in the whole R^N, with N >2. We study
both existence and multiplicity of radial ground state solutions for p>1,
emphasizing the fundamental difference between the subcritical and the
supercritical case. We also study speed decay at infinity of ground states, and
give some decay estimates. Finally we provide a multiplicity result on the
existence of sign-changing bound state solutions for any p>1.
