## Differential and Integral Equations

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

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

#### 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

**Permanent link to this document**

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