Multi-peak Positive Solutions To A Class Of Kirchhoff Equations In R~3

In this thesis,we consider the following Kirchhoff equation-(∈2α + ∈b∫R3|▽u|2dx)▽u+V(x)u =up,u>0,x∈R3,where a,b are positive constants,1<p<5 and ∈>0 is a parameter.Under some suit-able assumptions on the potential function V(x),applying the Lyapunov-Schmidt reduction method we prove that the equation above has a positive multi-peak solu-tion concentrating at a critical point of V(x)for ∈>0 sufficiently small.