UNIQUENESS AND ASYMPTOTIC-BEHAVIOR OF SOLUTIONS WITH BOUNDARY BLOW-UPFOR A CLASS OF NONLINEAR ELLIPTIC-EQUATIONS

We study the uniqueness and expansion properties of the positive solut ions u of (E) Delta u + hu - ku(p) = 0 in a non-smooth domain Omega, s ubject to the condition u (x) --> infinity when dist (x; partial deriv ative Omega) --> 0, where h and k are continuous functions in <(Omega) over bar>, k > 0 and p > 1. When partial derivative Omega has the loca l graph property, we prove that the solution is unique. When partial d erivative Omega has a singularity of conical or wedge-like type, we gi ve the asymptotic behavior of u. When partial derivative Omega has a r e-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.