Nondegeneracy of positive solutions to a Kirchhoff problem with critical Sobolev growth

In this paper, we prove uniqueness and nondegeneracy of positive solutions to the following Kirchhoff equations with critical growth −a+b∫R3|∇u|2Δu=u5,u>0inR3,where a,b>0 are positive constants. This result has potential applications in singular perturbation problems concerning Kirchhoff equations.