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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Behavior of positive radial solutions for quasilinear elliptic equations


Authors: Marta García-Huidobro, Raúl Manásevich and Cecilia S. Yarur
Journal: Proc. Amer. Math. Soc. 129 (2001), 381-388
MSC (2000): Primary 35A20, 35J60, 35B45; Secondary 34C11, 34D05
Published electronically: October 10, 2000
MathSciNet review: 1800231
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Abstract:

We establish a necessary and sufficient condition so that positive radial solutions to \begin{equation*}-{\rm div} (A(\vert\nabla u\vert)\nabla u) = f(u),\quad \mbox{in}~~ B_{R}(0)\setminus\{0\}, R>0, \end{equation*} having an isolated singularity at $x=0$, behave like a corresponding fundamental solution. Here, $A:\mathbb R\setminus \{0\}\to \mathbb R$ and $f:[0,\infty)\to[0,\infty)$are continuous functions satisfying some mild growth restrictions.


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Additional Information

Marta García-Huidobro
Affiliation: Departamento de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chile
Email: mgarcia@riemann.mat.puc.cl

Raúl Manásevich
Affiliation: Departamento de Ingeniería Matemática, Universidad de Chile, Casilla 170, Correo 3, Santiago, Chile
Email: manasevi@llaima.dim.uchile.cl

Cecilia S. Yarur
Affiliation: Departamento de Matemática y C. C., Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile
Email: cyarur@fermat.usach.cl

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05951-7
PII: S 0002-9939(00)05951-7
Keywords: Behavior, radial solutions, singular solutions, supersolutions
Received by editor(s): January 25, 1999
Published electronically: October 10, 2000
Additional Notes: The first author was sponsored by FONDECYT grant 1970332.
The second author was sponsored by FONDAP Matemáticas Aplicadas and FONDECYT grant 1970332.
The third author was sponsored by FONDAP Matemáticas Aplicadas, FONDECYT grant 1961235 and DICYT
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2000 American Mathematical Society