Radial symmetry of large solutions of nonlinear elliptic equations
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- by Steven D. Taliaferro PDF
- Proc. Amer. Math. Soc. 124 (1996), 447-455 Request permission
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
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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
- © Copyright 1996 American Mathematical Society
- 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