On The Uniqueness Of Multi-peak Solutions To A Class Of Kirchhoff Type Equations

In this paper,we study the uniqueness of multi-peak solutions to the following Kirchhoff type equations which concentrate at non-degenerate critical points of the potential function V(x),where ε>0 is a parameter,a,b>0,1<p<5 are constants.By using the local Pohozave identities,we prove the uniqueness of multi-peak solutions which concentrate at {ai}1≤i≤k where {ai}1≤i≤k are non-degenerate critical points of V(x)as ε→0.Our result extends a similar uniqueness result of multi-peak solutions to semi-linear equations obtained by P.Luo et al.in(arXiv:1909.08828v1,2019)to Kirchhoff type equations.