Positive minimizers of the best constants and solutions to coupled critical quasilinear systems

In this paper, systems of quasilinear elliptic equations are investigated, which involve critical homogeneous nonlinearities and deferent Hardy-type terms. By variational methods and careful analysis, positive minimizers of the related best Sobolev constants are found and the existence of positive solutions to the systems is verified. The results are new even in the case p=2p=2.