  We consider the singular boundary-value problem \Delta u = f(u) in D; u|_dD=
phi, where
  1. D is a bounded C^2-domain of R^d, d >= 3
  2. f: (0,1) -> (0,1) is a locally H\"older continuous function such that f(u)
-> 1 as u -> 0 at the rate u^{-\alpha}, for some \alpha in (0,1),
  3. and phi is a positive 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-bar. Such solutions are shown to
satisfy a boundary Harnack principle. Probabilistic techniques are used in
proving the main results.
