Perturbation results of critical elliptic equations of Caffarelli-Kohn-Nirenberg type

Abstract

We find for small E positive solutions to the equation A figure is presented. in ℝN, which branch off from the manifold of minimizers in the class of radial functions of the corresponding Caffarelli-Kohn-Nirenberg-type inequality. Moreover, our analysis highlights the symmetry-breaking phenomenon in these inequalities, namely the existence of non-radial minimizers. © 2003 Elsevier Science (USA). All rights reserved.