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On the uniqueness of singular solutions for a Hardy-Sobolev equation
1. | Department of Mathematics, National Central University, Chung-Li 32001, Taiwan |
2. | Department of Mathematics, Tamkang University, Tamsui 25137, Taiwan, Taiwan |
$\Delta u+u^p+\frac{u^{2^*(s)-1}}{|x|^s}=0 $ in $B_1 \setminus \left \{ 0 \right \},$
where $p>1, 0 < s < 2, 2^*(s)=\frac{2(n-s)}{n-2}$, $n\geq 3$ and $B_1$ is the unit ball in $ R^n$ centered at the origin. We prove that if $p>\frac{n+2}{n-2}$ then such solution is unique.
References:
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