Positive radial solutions for Dirichlet problem of quasilinear differential system with mean curvature operator in Minkowski space

Abstract

In this paper, we are considered with the Dirichlet problem of quasilinear differential system, involving the mean curvature operator in Minkowski space $$\begin{aligned} {\mathcal {M}}(w)=\text {div}\left( \frac{\nabla w}{\sqrt{1-|\nabla w|^2}}\right) , \end{aligned}$$ in a ball in $${\mathbb {R}}^N$$ . Using global bifurcation technique, we obtain the existence of an unbounded branch of positive radial solutions, which is unbounded in positive $$\lambda $$ -direction.