In this paper, we study the existence of entire positive solutions for the $k$-Hessian type equation

$${\mathrm{S}}_k(D^{2}u+\alpha I)=p(|x|)f^k(u),x\in {\mathbb{R}}^n$$

and system

$$\{\begin{array}{l}{\mathrm{S}}_k(D^{2}u+\alpha I)=p(|x|)f^k(v),x\in {\mathbb{R}}^n,\\ {\mathrm{S}}_k(D^{2}v+\alpha I)=q(|x|)g^k(u),x\in {\mathbb{R}}^n,\end{array}$$

where $D^{2}u$ is the Hessian of $u$ and $I$ denotes unit matrix. The arguments are based upon a new monotone iteration scheme.