Asymptotics of solutions of some nonlinear elliptic systems

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Abstract
This paper deals with the local and global behaviour of the postive solutions of the semilinear elliptic system in where and Our main result is the fact that the solutions satisfy Harnack inequality when , which gives local estimates. Without this assumption on Q, we give the precise behaviour of the solutions, provided that these estimates are true. when the solutions are asymptotically readial, but a symmetry bracking may occur between u and v, where u/v tends to 0 or infinity. Beyond the solutions can also present an anisotropic behaviour.