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

In this paper,we study the Kirchhoff problem-(ε2a+εb∫R2|▽u|2)△u+u=Q(x)|u|q--2u,x ∈R3,where a,b>0,2<q<6 are constants,ε:>0 is a parameter.Under some assumptions on the function Q(x),we obtain multi-peak solutions uε of the above problem by Lyapunov-Schmidt reduction method for sufficiently small ε.And we show that the solutions {uε} concentrate at a minimal point of Q(x).