Abstract
In this paper, we consider the following weighted PDE system with Navier boundary conditions on a half space:1 When is any even number between and , we establish the equivalence between (1) and the following integral system2 under some very mild growth condition, where is the reflection of the point about the plane . Then, in the critical case of , we show that every pair of positive solutions of system (2) is rotationally symmetric about -axis. While in the subcritical case, we prove the non-existence of positive solutions. When dealing integral system (2), can be any real number between and .
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