Multiplicity of positive radial solutions for systems with mean curvature operator in Minkowski space

Abstract

In this paper, we are considered with the Dirichlet problem of quasilinear differential system with mean curvature operator in Minkowski space $ \mathcal{M}(w): = \text{div}\Big(\frac{\nabla w}{\sqrt{1-|\nabla w|^2}}\Big), $ in a ball in $ \mathbb{R}^N $. In particular, we deal with this system with Lane-Emden type nonlinearities in a superlinear case, by using the Leggett-Williams' fixed point theorem, we obtain the existence of three positive radial solutions.