UNIQUENESS OF SOLUTIONS WITH BLOWUP AT THE BOUNDARY FOR A CLASS OF NONLINEAR ELLIPTIC-EQUATIONS

We prove that for any p > 1 there exists at most one positive function u satisfying DELTAu = u(p) in some domain OMEGA in R(N) and u(x) --> infinity, as dist (x, partial derivative OMEGA) --> 0, where partial d erivative OMEGA is compact and is locally the graph of a continuous fu nction defined on an (N - 1)-dimensional space. We also study the exis tence or the boundary behaviour of such a u according to the regularit y of partial derivative OMEGA.