Positive solutions to a singular Neumann problem

We show the existence of positive solution for the following class of singular Neumann problem in BR with ∂u/∂ν=0 on ∂BR, where R>0, λ>0 is a positive parameter, β>0, p∈[0,1), BR=BR(0)⊂RN, and are radially symmetric nonnegative C1 functions. Using variational methods and sub- and supersolutions, we obtain a solution for an approximated problem involving mixed boundary conditions. The limit of the approximated solutions, is a positive solution.