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

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

2002-03-20

arxiv.org/abs/math/0203208v3

Mathematics

Analysis of PDEs

15 pages, 4 figures

Scientific paper

We find for small $\epsilon$ positive solutions to the equation \[-\textrm{div} (|x|^{-2a}\nabla u)-\displaystyle{\frac{\lambda}{|x|^{2(1+a)}}} u= \Big(1+\epsilon k(x)\Big)\frac{u^{p-1}}{|x|^{bp}}\] in ${\mathbb{R}}^N$, 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.

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