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

We find for small positive solutions to the equation in , 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.