Studies On The Existence And Concentration Of Multi-peak Solutions To A Class Of Kirchhoff Type Equations

In this paper,we study the existence and concentration of multi-peak solutions to the following Kirchhoff type equations which concentrate at non-degenerate critical points of the potential function V(x),where ?>0 is a parameter,a,b>0,1<p<5 are constants.Applying the Lyapunov-Schmidt reduction method,we prove that if {ai}1?i?k are non-degenerate critical points of V(x),then there exist multi-peak solutions concentrating at {ai}1?i?k to the above equations as ?? 0.Our result extends a similar existence result of multi-peak solutions to semi-linear equations obtained by Peng Luo et al.in(arXiv:1909.08828v1,2019)to Kirchhoff type equations.