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By Castorina D., Fabbri I., Mancini G.

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Vol. 165 no. 1 (1999), pag. 117-149. E. Andrews, R. Askey, R. Roy, Special functions, Encyclopedia of Mathematics and its applications Vol. 71 (1999), Cambridge University press. [5] W. Beckner, On the Grushin operator and hyperbolic symmetry, Proc. Amer. Math. Soc. Vol. 129 (2001), pag. 1233-1246. [6] M. Badiale, E. Serra, Critical nonlinear elliptic equations with singularities and cylindrical symmetry, Rev. Mat. Iberoamericana Vol. 1 (2004), pag. 33-66. Tarantello, A Sobolev-Hardy inequality with applications to a nonlinear elliptic equation arising in astrophysics, Arch.

4) assures that Φε has a maximum or minimum and hence a critical point converging to (λ0 , ζ0 ) ∈ (0, ∞) × Rh as ε → 0. 1 we get multiplicity. Proof of Theorem B. We follow closely [20], where the Authors prove a similar result for the Webster scalar curvature problem on the CR sphere. The theorem can be established through the above finite dimensional reduction and a topological degree argument, namely proving that there exist an open set Ω ⊂ R+ × Rh such that deg(∇Γ, Ω, 0) = 0. We start proving that the critical points of the Melnikov function Γ(λ, ζ) = N −2 2(N − 1) RN −1) ϕ(λy, λz + ζ) 2(N U N −2 |y| lay in a bounded region λ2 + |ζ|2 ≤ R.

Non lin. Vol. 19 no 3 (2002), pag. 313-342. [3] A. Ambrosetti, J. Garcia Azorero, I. Peral, Perturbation of ∆u + u(N +2)/(N −2) = 0, the scalar curvature problem in RN , and related topics, J. Funct. Anal. Vol. 165 no. 1 (1999), pag. 117-149. E. Andrews, R. Askey, R. Roy, Special functions, Encyclopedia of Mathematics and its applications Vol. 71 (1999), Cambridge University press. [5] W. Beckner, On the Grushin operator and hyperbolic symmetry, Proc. Amer. Math. Soc. Vol. 129 (2001), pag. 1233-1246.

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