Existence and uniqueness of positive large solutions to some cooperative elliptic systems

In this work we consider positive solutions to cooperative elliptic systems of the form -Deltau = lambdau-u(2) +bunu, -Deltanu = munu-nu(2)+cunu in a bounded smooth domain Omega subset of R-N (lambda, mu is an element of R, b, c > 0) which blow up on the boundary an, that is u(x), nu(x) --> +infinity as dist(x, partial derivativeOmega) --> 0. We show existence and nonexistence of solutions, and give sufficient conditions for uniqueness. We also provide an exact estimate of the behaviour of the solutions near the boundary in terms of dist(x, partial derivativeOmega).