We study the existence and the multiplicity of solutions for the problem - div (p (x) ∇ u) = u2*- 1+ λ u, u > 0 in Ω and u = 0 on ∂Ω, when the set of the minimizers for the weight p has multiple connected component. We study also the case where this set has one connected component and has complex topology. To cite this article: R. Hadiji et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006). © 2006 Académie des sciences.
Hadiji, R., Molle, R., Passaseo, D., & Yazidi, H. (2006). Localization of solutions for nonlinear elliptic problems with critical growth. Comptes Rendus Mathematique, 343(11–12), 725–730. https://doi.org/10.1016/j.crma.2006.10.018