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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Uniqueness of positive solutions for singular problems involving the $p$-Laplacian
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by Arkady Poliakovsky and Itai Shafrir PDF
Proc. Amer. Math. Soc. 133 (2005), 2549-2557 Request permission

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
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2146198