Full paper in PDF:
$% B. Abdellaoui, V. Felli, and I. Peral, A remark on perturbed elliptic equations of Caffarelli-Kohn-Nirenberg type, Rev. Mat. Complut. 18 (2005), no. 2, 339–351.%$

A Remark on Perturbed Elliptic Equations of Caffarelli-Kohn-Nirenberg Type

Boumediene ABDELLAOUI 1, Veronica FELLI 2,
and Ireneo PERAL 1
1Departamento de Matemáticas
Universidad Autónoma de Madrid
Cantoblanco 28049, Madrid — Spain.
boumediene.abdellaoui@uam.es

ireneo.peral@uam.es.

2Dipartimento di Matematica e Applicazioni
Università di Milano Bicocca
Via Bicocca degli Arcimboldi 8
20126 Milano — Italy.
felli@matapp.unimib.it.

Received: December 21, 2004
Accepted: February 14, 2005
ABSTRACT

Using a perturbation argument based on a finite dimensional reduction, we find positive solutions to the following class of perturbed degenerate elliptic equations with critical growth

-2a --c---- up-1 N -div(|x| (I + eB(x)) \~/ u) - |x|2(1+a) u= |x|bp, x (- R

where - oo <a < N-22- , ( ) - oo < c < N-22a- 2-2 , p= p(a,b) = N-22(1N+a-b) , and a < b< a+ 1 .

Key words: semilinear elliptic equations, critical Sobolev exponent, Caffarelli-Kohn-Nirenberg inequalities.
2000 Mathematics Subject Classification: 35J70, 35J20, 35B33, 35B20.