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Proceedings of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0002-9939-05-07290-4
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: $-\Delta _p{u}-\lambda \eta (x)\frac {{u}^{p-1}}{|x|^p} = \mu \frac {{u}^{p-1}}{|x|^p}$ on a bounded smooth domain $\Omega \subset \mathbb {R}^N$ with zero boundary condition. We also characterize all positive solutions of $-\Delta _p{u}=|\frac {N-p}{p}|^p \frac {u^{p-1}}{|x|^p}$ 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

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.