On a singular semilinear elliptic boundary value problem and the boundary Harnack principle

On a bounded C-2-domain D subset of R-d we consider the singular boundary-value problem 1/2 Deltau = f (u) in D, u|partial derivative(D) = phi, where d greater than or equal to 3, f : (0, infinity) --> (0, infinity) is a locally Holder continuous function such that f(u) --> infinity as u --> 0 at the rate u(-alpha), for some alpha is an element of (0, 1), and phi is a non-negative continuous function satisfying certain growth assumptions. We show existence of solutions bounded below by a positive harmonic function, which are smooth in D and continuous in (D) over bar. D. Such solutions are shown to satisfy a boundary Harnack principle.