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Radial symmetry of large solutions of nonlinear elliptic equations


Author: Steven D. Taliaferro
Journal: Proc. Amer. Math. Soc. 124 (1996), 447-455
MSC (1991): Primary 35J60
DOI: https://doi.org/10.1090/S0002-9939-96-03372-2
MathSciNet review: 1327049
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Abstract | References | Similar Articles | Additional Information

Abstract: We give conditions under which all $C^2$ solutions of the problem \begin{align*} &\Delta u = f(|x|,u),\qquad x\in {\mathbb {R}}^n,\ &\lim _{|x|\to \infty } u(x) = \infty \end{align*} are radial. We assume $f(|x|,u)$ is positive when $|x|$ and $u$ are both large and positive. Since this problem with $f(|x|,u) = u$ has non-radial solutions, we rule out this possibility by requiring that $f(|x|,u)$ grow superlinearly in $u$ when $|x|$ and $u$ are both large and positive. However we make no assumptions on the rate of growth of solutions.


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

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Additional Information

Steven D. Taliaferro
Affiliation: Mathematics Department, Texas A&M University, College Station, Texas 77843
Email: stalia@math.tamu.edu

Received by editor(s): July 22, 1994
Communicated by: Jeffrey Rauch
Article copyright: © Copyright 1996 American Mathematical Society