Abstract
The aim of this paper is to prove the nondegeneracy of the unique positive solutions for the following critical Hartree type equations when μ>0 is close to 0, −Δu=Iμ∗u2μ∗u2μ∗−1,x∈RN, where Iμ(x)=Γ(μ2)Γ(N−μ2)πN22N−μ|x|μ is the Riesz potential and 2μ∗=2N−μN−2 is the upper critical exponent due to the Hardy–Littlewood–Sobolev inequality.
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