Abstract
In this paper, we study the existence of solutions to the problem(−Δ)n/2u=enuonRn﹨{0},Λ=∫Rnenudx<∞ for n≥3, which corresponds to finding singular conformal metrics gu:=e2u|dx|2 on Rn﹨{0} with constant Q-curvature equal to one and finite volume Λ. We prove that under suitable conditions, the above equation admits a (nonradial) solution with prescribed polynomial behaviors at zero and infinity. The mass Λ and asymptotic behaviors of solution u can be simultaneously prescribed. This extends results of König-Laurain and Hyder-Mancini-Martinazzi.
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