Abstract
, (1.12)where Q = −P.If k = 1, v is a radially symmetric (with respect to Q) solution of (1.12)The proofs of our results make use of ideas in the new proof of the Liouville-type theorem of Caffarelli, Gidas and Spruck ([6]; see also Gidas, Ni and Nirenberg[12] for the result under some decay assumption near infinity) given in [15] and [14],which is based on the method of moving planes and full exploitation of the conformalinvariance of the problem.2. Preliminary results. In this section we present some results which will beused in the proofs of Theorem 1.1 and Theorem 1.3.Denote B
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