Large and very singular solutions to semilinear elliptic equations

We consider equation -Delta u f(x, u) = 0 in smooth bounded domain Omega is an element of R-N, N >= 2, with f (x, r) > 0 in Omega x R-+(1) + and f(x, r) = 0 on partial derivative Omega. We find the condition on the order of degeneracy of f (x, r) near partial derivative Omega, which is a criterion of the existence-nonexistence of a very singular solution with a strong point singularity on partial derivative Omega. Moreover, we prove that the mentioned condition is a sufficient condition for the uniqueness of a large solution and conjecture that this condition is also a necessary condition of the uniqueness.