On a prescribed mean curvature equation in Lorentz-Minkowski space

TL;DR

This paper investigates the existence, multiplicity, and decay properties of solutions to a prescribed mean curvature equation in Lorentz-Minkowski space, highlighting differences between subcritical and supercritical cases.

Contribution

It provides new results on solution existence, multiplicity, and decay estimates for the prescribed mean curvature equation in Lorentz-Minkowski space, including sign-changing solutions.

Findings

Existence of radial ground state solutions for p>1

Decay estimates for solutions at infinity

Multiplicity of sign-changing bound state solutions

Abstract

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.