Abstract
In this paper, we study the following problem(P){(−Δ)su=|u|2s⁎−2u+λu, in Ω,u=0, in RN∖Ω, where 2s⁎=2NN−2s, s>12, Ω is a bounded domain in RN, N>2s. We first show that if λ>0 is small, single bubbling solutions of (P) concentrating at a non-degenerate critical point of the Robin function is non-degenerate provided N≥4s+1. Then, using this result, we prove that if N∈[4s+1,6s] and Ω is a ball, (P) has infinitely many sign-changing bubbling solutions, whose energy can be arbitrarily large.
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