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

In this paper,we study the Kirchhoff problem-(?2a+?b?R2|?u|2)?u+u=Q(x)|u|q--2u,x ?R3,where a,b>0,2<q<6 are constants,?:>0 is a parameter.Under some assumptions on the function Q(x),we obtain multi-peak solutions u? of the above problem by Lyapunov-Schmidt reduction method for sufficiently small ?.And we show that the solutions {u?} concentrate at a minimal point of Q(x).