Arbitrarily large solutions of the conformal scalar curvature problem at an isolated singularity

Abstract

We study the conformal scalar curvature problem k(x)u n+2/n-2 ≤ -Δu ≤ u n+2/n-2 in R n , n ≥ 3 where k : R n → (0,1] is a continuous function. We show that a necessary and sufficient condition on k for this problem to have C 2 positive solutions which are arbitrarily large at ∞ is that k be less than 1 on a sequence of points in Rn which tends to ∞.