ON THE UNIQUENESS OF SINGULAR SOLUTIONS FOR A HARDY-SOBOLEV EQUATION

摘要

In this paper, we consider the positive singular solutions for the following Hardy-Sobolev equation △u + u~p + u~(2*(s)-1)/|x|~s = 0 in B1 {0}, where p > 1, 0 < s < 2, 2*(s) = 2(n-s)/n-2, n > 3 and B1 is the unit ball in R~n centered at the origin. We prove that if p > n+2/n-2 then such solution is unique.