We consider the following nonlinear singular elliptic equation
84.0ptnormalΔu(x)+f(x,ufalse(xfalse))−b(x)false(u(x)false)−αfalse∥∇u(x)false∥β+g(x)x·∇u(x)=00.33em0.33emin0.33em0.33emnormalΩ,\begin{equation*}\hskip7pc \Delta u(x)+f(x,u(x))-b(x)(u(x))^{-\alpha }\Vert \nabla u(x)\Vert ^{\beta }+ g(x)x\cdot \nabla u(x)=0 \ \ \text{in} \ \ \Omega ,\hskip-7pc \end{equation*}where n>2$n>2$, normalΩ:=false{x∈Rn;0.16emfalse∥xfalse∥>Rfalse}$\Omega :=\lbrace x\in \mathbb {R}^{n};\,\Vert x\Vert >R \rbrace$. Our main purpose is to prove the existence of a large number of positive solutions with the asymptotic decay u(x)=Otrue(false∥xfalse∥2−ntrue)$u(x)=O\big (\Vert x\Vert ^{2-n}\big )$ as false∥xfalse∥→∞$\Vert x\Vert \rightarrow \infty$. We also investigate the rate of decay of ∇u$\nabla u$. These results are based on the sub and supersolution method and cover both sublinear and superlinear cases of f.