We investigate the asymptotic behavior of positive solutions to the elliptic equation (0.1) ${Delta}u+|x|^{l_1}u^p+|x|^{l_2}u^q=0$ in $mathbb{R}^n$. We obtain a conclusion that, for n $geq$ 3, -2 < $l_2$ < $l_1$ $leq$ 0 and q > p > 1, any positive radial solution to (0.1) has the following properties: $lim_{r{ ightarrow}{infty}}r^{frac{2+l_1}{p-1}};u$ and $lim_{r{ ightarrow}0}r^{frac{2+l_2}{q-1}};u$ always exist if $frac{n+1_1}{n-2}$ < p < q, $p;{ eq};frac{n+2+2l_1}{n-2}$, $q;{ eq};frac{n+2+2l_2}{n-2}$. In addition, we prove that the singular positive solution of (0.1) is unique under some conditions.