Advances in Differential Equations

On positive entire solutions to a class of equations with a singular coefficient and critical exponent

Susanna Terracini

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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.

Article information

Source
Adv. Differential Equations, Volume 1, Number 2 (1996), 241-264.

Dates
First available in Project Euclid: 25 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366896239

Mathematical Reviews number (MathSciNet)
MR1364003

Zentralblatt MATH identifier
0847.35045

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)

Citation

Terracini, Susanna. On positive entire solutions to a class of equations with a singular coefficient and critical exponent. Adv. Differential Equations 1 (1996), no. 2, 241--264. https://projecteuclid.org/euclid.ade/1366896239


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