a population biological model with a singular nonlinearity and caffarelli-kohn-nirenberg exponents

We consider the existence of positive solutions of singular nonlinear semipositone problem of the form [left{begin{array}{ll} -div(|x|^{-alpha p}|nabla u|^{p-2}nabla u)=|x|^{-(alpha+1)p+beta}(au^{p-1}-bu^{r}-f(u)-frac{c}{u^{gamma}}), & xinomega, u=0, & xinpartialomega, end{array}right.]where $omega$ is a bounded domain in ${mathbb{r}}^{n}$ with smooth boundary $partialomega$, $1p-1 $,$gammain (0,1)$, $a,b,c,beta$ are positive parameters, and $f:[0,+infty)to{mathbb{r}}$ is a continuous function . this model arises in the studies of population biology of one specieswith u representing the concentration of the species. we obtain our results via the method of sub and supersolutions.