## Differential and Integral Equations

### Solutions of semilinear elliptic equations with one isolated singularity

Yomna Rébaï

#### 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.

#### Article information

Source
Differential Integral Equations, Volume 12, Number 4 (1999), 563-581.

Dates
First available in Project Euclid: 29 April 2013

https://projecteuclid.org/euclid.die/1367267007

Mathematical Reviews number (MathSciNet)
MR1697245

Zentralblatt MATH identifier
1064.35510

Subjects
Primary: 35J60: Nonlinear elliptic equations

#### Citation

Rébaï, Yomna. Solutions of semilinear elliptic equations with one isolated singularity. Differential Integral Equations 12 (1999), no. 4, 563--581. https://projecteuclid.org/euclid.die/1367267007