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.
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