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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 | References | Similar Articles | Additional Information


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.

References [Enhancements On Off] (What's this?)

  • 1. M. García-Huidobro, R. Manásevich and C. S. Yarur, On Positive Singular Solutions for a Class of Non Homogeneous $p$-Laplacian like Equations, Journal of Differential Equations, 147, N. 1 (1998) 23-51. MR 99a:35065
  • 2. M. Guedda and L. Veron, Local and Global properties of solutions of Quasilinear Elliptic Equations, Journal of Differential Equations 75 (1988), 441-550.
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Additional Information

Marta García-Huidobro
Affiliation: Departamento de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chile

Raúl Manásevich
Affiliation: Departamento de Ingeniería Matemática, Universidad de Chile, Casilla 170, Correo 3, Santiago, Chile

Cecilia S. Yarur
Affiliation: Departamento de Matemática y C. C., Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile

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

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