THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK SOLUTIONS TO A CLASS OF KIRCHHOFF TYPE EQUATIONS

In this paper, we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations -(ε2a + εb∫R3|?u|2)?u + V(x)u = up, u > 0 in R3,which concentrate at non-degenerate critical points of the potential function V(x), where a, b >0, 1 < p < 5 are constants, and ε > 0 is a parameter. Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity, we establish the existence and local uniqueness results 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.