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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Uniqueness of positive solutions for singular problems involving the $p$-Laplacian


Authors: Arkady Poliakovsky and Itai Shafrir
Journal: Proc. Amer. Math. Soc. 133 (2005), 2549-2557
MSC (2000): Primary 35J70; Secondary 49R50
Published electronically: April 12, 2005
MathSciNet review: 2146198
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Abstract: We study existence and uniqueness of positive eigenfunctions for the singular eigenvalue problem: $-\Delta_p{u}-\lambda\eta(x)\frac{{u}^{p-1}}{\vert x\vert^p} = \mu\frac{{u}^{p-1}}{\vert x\vert^p}$ on a bounded smooth domain $\Omega\subset\mathbb{R} ^N$ with zero boundary condition. We also characterize all positive solutions of $-\Delta_p{u}=\vert\frac{N-p}{p}\vert^p \frac{u^{p-1}}{\vert x\vert^p}$ in $\mathbb{R} ^N\setminus\{0\}$.


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Additional Information

Arkady Poliakovsky
Affiliation: Department of Mathematics, Technion - Israel Institute of Technology, 32000 Haifa, Israel
Email: maarkady@tx.technion.ac.il

Itai Shafrir
Affiliation: Department of Mathematics, Technion - Israel Institute of Technology, 32000 Haifa, Israel
Email: shafrir@tx.technion.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07290-4
PII: S 0002-9939(05)07290-4
Received by editor(s): March 2, 2002
Published electronically: April 12, 2005
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.