Singular Yamabe-type problems with an asymptotically flat metric

In this paper, we study the asymptotic symmetry and local behavior of positive solutions at infinity to the equation -Lgu = |x|τun+2+2τ/n-2 outside a bounded set in Rⁿ , where n≥ 3 , -2<τ<0 , and Lg is the conformal Laplacian with asymptotically flat Riemannian metric g . We prove that the solution, at ∞ , either converges to a fundamental solution of the Laplace operator on the Euclidean space, or is asymptotically close to a Fowler-type solution defined on Rⁿ \{0\} .