Abstract
For the equation − Δ u = | | x | − 2 | α u p − 1 , 1 < | x | < 3 , we prove the existence of two solutions for α large, and of two additional solutions when p is close to the critical Sobolev exponent 2 ∗ = 2 N / ( N − 2 ) . A symmetry-breaking phenomenon appears, showing that the least-energy solutions cannot be radial functions.
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