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On the uniqueness of singular solutions for a Hardy-Sobolev equation

Pages: 123 - 128, Issue special, November 2013

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Jann-Long Chern - Department of Mathematics, National Central University, Chung-Li 32001, Taiwan (email)
Yong-Li Tang - Department of Mathematics, National Central University, Chung-Li 32001, Taiwan (email)
Chuan-Jen Chyan - Department of Mathematics, Tamkang University, Tamsui 25137, Taiwan (email)
Yi-Jung Chen - Department of Mathematics, Tamkang University, Tamsui 25137, Taiwan (email)

Abstract: In this paper, we consider the positive singular solutions for the following Hardy-Sobolev equation
                        $\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.

Keywords:  Hardy-Sobolev equation, singular solution, uniqueness of solutions.
Mathematics Subject Classification:  Primary: 35J60; Secondary: 35A02.

Received: September 2012;      Revised: February 2013;      Published: November 2013.

 References