## Advances in Differential Equations

- Adv. Differential Equations
- Volume 2, Number 3 (1997), 383-402.

### Classification of positive singular solutions for a class of semilinear elliptic systems

Marta García-Huidobro and Cecilia S. Yarur

#### Abstract

This paper is concerned with the behavior near an isolated singularity of positive radial solutions of the semilinear elliptic system $$ \begin{cases} -\Delta u=\vert v\vert^{p-1}v \\ -\Delta v=\vert u\vert^{q-1}u, \end{cases} \text{in}\ \ \Omega^*\subset\Bbb R^N, $$ where $\Omega^*$ denotes the punctured unit ball in $\Bbb R^N\ (N\ge 3)$ and $(p,q)$ lies in the region between the two critical hyperbolas $\mathcal{H}_1$ and $\mathcal{H}_2$ defined below.

#### Article information

**Source**

Adv. Differential Equations, Volume 2, Number 3 (1997), 383-402.

**Dates**

First available in Project Euclid: 23 April 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.ade/1366742249

**Mathematical Reviews number (MathSciNet)**

MR1441849

**Zentralblatt MATH identifier**

1023.35504

**Subjects**

Primary: 35J60: Nonlinear elliptic equations

Secondary: 34A34: Nonlinear equations and systems, general 35B05: Oscillation, zeros of solutions, mean value theorems, etc.

#### Citation

García-Huidobro, Marta; Yarur, Cecilia S. Classification of positive singular solutions for a class of semilinear elliptic systems. Adv. Differential Equations 2 (1997), no. 3, 383--402. https://projecteuclid.org/euclid.ade/1366742249