Proceedings of the American Mathematical Society

Author(s): Jorge García-Melián
Journal: Proc. Amer. Math. Soc. 135 (2007), 2785-2793.
MSC (2000): Primary 35J25; Secondary 35J60
Posted: March 30, 2007
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Abstract: In this paper, we prove that for

the problem $\Delta u=a(x)u^p$ in a bounded

domain $\Omega$ of $\mathbb{R}^N$ has a unique positive solution with $u=\infty$ on $\partial\Omega$ . The nonnegative weight

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

near $\partial\Omega$ was imposed.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35J25, 35J60

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

DOI: 10.1090/S0002-9939-07-08822-3
PII: S 0002-9939(07)08822-3
Received by editor(s): May 8, 2006
Posted: March 30, 2007
Additional Notes: Supported by MEC and FEDER under grant MTM2005-06480.
Communicated by: David S. Tartakoff
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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