Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Behavior of positive radial solutions for quasilinear elliptic equations

Author(s): Marta García-Huidobro; Raúl Manásevich; Cecilia S. Yarur
Journal: Proc. Amer. Math. Soc. 129 (2001), 381-388.
MSC (2000): Primary 35A20, 35J60, 35B45; Secondary 34C11, 34D05
Posted: October 10, 2000
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract | References | Similar articles | Additional information

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.

References:

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.

3.
P. L. Lions, Isolated Singularities in Semilinear Problems, Journal of Differential Equations 38 (1980), 441-550. MR 82g:35040

4.
W.-M. Ni and J. Serrin, Non-existence theorems for singular solutions of quasilinear partial differential equations, Communications in Pure and Applied Mathematics 39 (1986), 379-399. MR 87h:35116

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35A20, 35J60, 35B45, 34C11, 34D05

Retrieve articles in all Journals with MSC (2000): 35A20, 35J60, 35B45, 34C11, 34D05

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: 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
Posted: 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
Copyright of article: Copyright 2000, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google