Positive solutions to a singular Neumann problem

We show the existence of positive solution for the following class of singular Neumann problem − Δ u + a ( x ) u β = λ h ( x ) u p in B R with ∂ u / ∂ ν = 0 on ∂ B R , where R > 0 , λ > 0 is a positive parameter, β > 0 , p ∈ [ 0 , 1 ) , B R = B R ( 0 ) ⊂ R N , a : B R → R and h : B R → R are radially symmetric nonnegative C 1 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.