Uniqueness and asymptotic behavior of solutions with boundary blow-up for a class of nonlinear elliptic equations

We study the uniqueness and expansion properties of the positive solutions u of (E) Delta u + hu - ku(p) = 0 in a non-smooth domain Omega, subject to the condition u (x) --> infinity when dist (x; partial derivative Omega) --> 0, where h and k are continuous functions in <(Omega)over bar>, k > 0 and p > 1. When partial derivative Omega has the local graph property, we prove that the solution is unique. When partial derivative Omega has a singularity of conical or wedge-like type, we give the asymptotic behavior of u. When partial derivative Omega has a re-entrant cuspidal singularity, we prove that the rate of blow-up may not be of the same order as in the previous more regular cases.