## Advances in Differential Equations

- Adv. Differential Equations
- Volume 3, Number 1 (1998), 111-132.

### On the existence of positive solutions for a class of singular elliptic equations

Monica Conti, Stefano Crotti, and David Pardo

#### Abstract

We consider the class of equations $$ -\Delta u={A\over {|x|^{\alpha}}}u+u^{\theta} \qquad\qquad x\in\Bbb R^n\setminus\{0\} $$ where $A\in \Bbb R$, $\alpha>0$ and $\theta>1$. Depending on the values of the three parameters involved, we obtain both results of existence and nonexistence of positive solutions by combining the moving planes and the moving spheres methods through the Kelvin's inversion map and classical arguments on ODE's.

#### Article information

**Source**

Adv. Differential Equations Volume 3, Number 1 (1998), 111-132.

**Dates**

First available in Project Euclid: 19 April 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.ade/1366399907

**Mathematical Reviews number (MathSciNet)**

MR1608006

**Zentralblatt MATH identifier**

0944.35024

**Subjects**

Primary: 35J60: Nonlinear elliptic equations

Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc.

#### Citation

Conti, Monica; Crotti, Stefano; Pardo, David. On the existence of positive solutions for a class of singular elliptic equations. Adv. Differential Equations 3 (1998), no. 1, 111--132.https://projecteuclid.org/euclid.ade/1366399907