Positive radial solutions for systems with mean curvature operator in Minkowski space

Abstract

We are concerned with a Dirichlet system, involving the mean curvature operator in Minkowski space M(w) = div (∇w / 1−|∇w|2) in a ball in RN. Using topological degree arguments, critical point theory and lower and upper solutions method, we obtain non existence, existence and multiplicity of radial, positive solutions. The examples we provide involve Lane-Emden type nonlinearities in both sublinear and superlinear cases.