Advances in Differential Equations

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

Monica Conti, Stefano Crotti, and David Pardo

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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

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

First available in Project Euclid: 19 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc.


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.

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