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1996 On positive entire solutions to a class of equations with a singular coefficient and critical exponent
Susanna Terracini
Adv. Differential Equations 1(2): 241-264 (1996).

Abstract

We prove some results about existence, uniqueness and qualitative behavior of positive solutions to equations of the type $$ -\Delta u=a(x/|x|){u\over |x|^2}+f(x,u)\qquad\;\;\hbox{in }\;\mathbf{R}^n\setminus\{0\}\;,\tag 0.1 $$ depending on the behavior of the function $a$ of the angular variable $x/|x|$. Our main results concern the critical nonlinearity $f(s)=s^{(n+2)/(n-2)}$. The proofs are based on variational arguments and the moving plane method.

Citation

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Susanna Terracini. "On positive entire solutions to a class of equations with a singular coefficient and critical exponent." Adv. Differential Equations 1 (2) 241 - 264, 1996.

Information

Published: 1996
First available in Project Euclid: 25 April 2013

zbMATH: 0847.35045
MathSciNet: MR1364003

Subjects:
Primary: 35J60
Secondary: 35B05 , 58E05

Rights: Copyright © 1996 Khayyam Publishing, Inc.

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Vol.1 • No. 2 • 1996
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