We are concerned with the following mean curvature problem in Minkowski space \(\begin{aligned} \left\{ \begin{array}{ll} -\text {div}\bigg (\frac{\nabla v}{\sqrt{1-|\nabla v|^2}}\bigg )=\lambda m(|x|)f(v)~~\ \ \ & \text {in}\ {\mathbb {R}}^N,\\ v(|x|)\rightarrow 0& \text {as}\ |x|\rightarrow +\infty , \end{array} \right. \end{aligned}\) where \(N\ge 3\) , \(\lambda >0\) is a parameter, \(m\in C_{\text {loc}}^\alpha ({\mathbb {R}}^N, {\mathbb {R}})\) for some \(\alpha \in (0, 1)\) is a weighted function and \(f\in C({\mathbb {R}}, {\mathbb {R}})\) . Depending on the behavior of f near 0 and infinity, we investigate the existence and multiplicity of one-sign or sign-changing radial solutions to the problem. Moreover, we also obtain the rate of decay of solutions at \(\infty \) . The proof of the main results is based upon the bifurcation technique.
