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 del.[del u/root 1 - vertical bar del u vertical bar(2)] + u(p) = 0, set in the whole R-N, 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. (C) 2016 Elsevier Masson SAS. All rights reserved.