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.
Felli, V., & Schneider, M. (2003). Perturbation results of critical elliptic equations of Caffarelli-Kohn-Nirenberg type. Journal of Differential Equations, 191(1), 121–142. https://doi.org/10.1016/S0022-0396(02)00085-2