Positive solutions of the Dirichlet problem for the prescribed mean curvature equation in Minkowski space

Abstract

We prove the existence of multiple positive solutions of the Dirichlet problem for the prescribed mean curvature equation in Minkowski space {−div(∇u/1−|∇u|2)=f(x,u,∇u)in Ω,u=0on ∂Ω. Here Ω is a bounded regular domain in RN and the function f=f(x,s,ξ) is either sublinear, or superlinear, or sub-superlinear near s=0. The proof combines topological and variational methods.