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1999 Solutions of semilinear elliptic equations with one isolated singularity
Yomna Rébaï
Differential Integral Equations 12(4): 563-581 (1999).

Abstract

If $f$ is either given by $(1+u)^p$ for some $\frac{N+2}{N-2}< p < \frac{N+1}{N-3}$, $N\geq 3$ or if $f$ is given by $e^u$ when $N=3$, we prove the existence of a positive weak solution of $ \Delta u + \lambda f(u) =0 $ which is defined in the unit ball of ${\Bbb R}^N$, has $0$ boundary data and has a nonremovable prescribed singularity at some point $x_0$ close to the origin.

Citation

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Yomna Rébaï. "Solutions of semilinear elliptic equations with one isolated singularity." Differential Integral Equations 12 (4) 563 - 581, 1999.

Information

Published: 1999
First available in Project Euclid: 29 April 2013

zbMATH: 1064.35510
MathSciNet: MR1697245

Subjects:
Primary: 35J60

Rights: Copyright © 1999 Khayyam Publishing, Inc.

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Vol.12 • No. 4 • 1999
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