1998 On the existence of positive solutions for a class of singular elliptic equations
Monica Conti, Stefano Crotti, David Pardo
Adv. Differential Equations 3(1): 111-132 (1998). DOI: 10.57262/ade/1366399907

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.

Citation

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Monica Conti. Stefano Crotti. David Pardo. "On the existence of positive solutions for a class of singular elliptic equations." Adv. Differential Equations 3 (1) 111 - 132, 1998. https://doi.org/10.57262/ade/1366399907

Information

Published: 1998
First available in Project Euclid: 19 April 2013

zbMATH: 0944.35024
MathSciNet: MR1608006
Digital Object Identifier: 10.57262/ade/1366399907

Subjects:
Primary: 35J60
Secondary: 35B05

Rights: Copyright © 1998 Khayyam Publishing, Inc.

Vol.3 • No. 1 • 1998
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