Positive solutions of the p-Laplace equation with singular nonlinearity

For a given bounded domain Ω in Rn with C1,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 −Δpu=f(x,u) admits a solution . On the basis of a comparison principle we will give a sufficient condition under which such a problem admits a unique solution.