Positive solutions of the p-Laplace equation with singular nonlinearity

For a given bounded domain Ω in R n with C 1 , ϖ boundary for some 0 < ϖ < 1 , and a possibly singular nonlinearity f on Ω × ( 0 , ∞ ) , we give sufficient conditions on f so that the p-Laplace equation − Δ p u = f ( x , u ) admits a solution u ∈ W 0 1 , p ( Ω ) . On the basis of a comparison principle we will give a sufficient condition under which such a problem admits a unique solution.