On a prescribed mean curvature equation in Lorentz–Minkowski space

We are interested in providing new results on the following prescribed mean curvature equation in Lorentz–Minkowski space∇⋅[∇u1−|∇u|2]+up=0, set in the whole RN, with N⩾3. We study both existence and multiplicity of radial ground state solutions (namely positive and vanishing at infinity) 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.