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

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

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.