## 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 $\mathbb {R}^N\setminus \{0\}$.## References

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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