Uniqueness for boundary blow-up problems with continuous weights
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Abstract:
In this paper, we prove that for $p>1$ the problem $\Delta u=a(x)u^p$ in a bounded $C^2$ domain $\Omega$ of $\mathbb R^N$ has a unique positive solution with $u=\infty$ on $\partial \Omega$. The nonnegative weight $a(x)$ is continuous in $\overline {\Omega }$, but is only assumed to verify a “bounded oscillations" condition of local nature near $\partial \Omega$, in contrast with previous works, where a definite behavior of $a$ near $\partial \Omega$ was imposed.References
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Additional Information
- Jorge García-Melián
- Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna, C/ Astrofísico Francisco Sánchez s/n, 38271, La Laguna, Spain
- Email: jjgarmel@ull.es
- Received by editor(s): May 8, 2006
- Published electronically: March 30, 2007
- Additional Notes: Supported by MEC and FEDER under grant MTM2005-06480.
- Communicated by: David S. Tartakoff
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 2785-2793
- MSC (2000): Primary 35J25; Secondary 35J60
- DOI: https://doi.org/10.1090/S0002-9939-07-08822-3
- MathSciNet review: 2317953