The study reveals uniqueness and nondegeneracy of positive solutions in critical fractional Kirchhoff equations, indicating implications for singular perturbation problems.
In this paper, we consider the following critical fractional Kirchhoff equation {equation*} (a+b{∫_{RN}}|(-Δ)s/2u|^2dx)(-Δ)^su=|u|2^*_s-2u, in\ RN, {equation*} where $a,b>0$, N/4<s<1, 2^*ₛ=2N/N-2s and (-Δ )ˢ is the fractional Laplacian. We prove the uniqueness and nondegeneracy of positive solutions to the problem, which can be used to study the singular perturbation problems concerning fractional Kirchhoff equations.
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Yang et al. (2025) studied this question.
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