In this paper, we show how changes in the sign of nonlinearity leads to multiple radial ground state solutions of the mean curvature equation \( \nabla\cdot \Big[\frac{\nabla u}{\sqrt{1-|\nabla u|^2}}\Big] +\lambda f(u)=0\ \ \text{in} \ \mathbb{R}^N \) for sufficiently large \(\lambda\) with \(N\geq 2\).