Abstract: In this paper, we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations
$\begin{equation*} -\left(\varepsilon^2 a+\varepsilon b\int_{\mathbb R^3}|\nabla u|^2\right)\Delta u +V(x)u =u^{p}, u>0 \text{in} \mathbb{R}^3, \end{equation*}$
which concentrate at non-degenerate critical points of the potential function $V(x)$, where $a,b>0$, $1<p<5$ are constants, and $\varepsilon>0$ 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 $\{a_i\}_{1\leq i\leq k}$, where $\{a_{i}\}_{1\leq i\leq k}$ are non-degenerate critical points of $V(x)$ as $\varepsilon\to 0$.

Key words: Kirchhoff type equations, potential functions having non-degenerate critical points, the Lyapunov-Schmidt reduction method, multi-peak solutions, existence and local uniqueness