We consider the following singularly perturbed Kirchhoff-type equations
$$\begin{aligned} -\varepsilon ^2 M\left( \varepsilon ^{2-N}\int _{{\mathbb {R}}^N}|\nabla u|^2 \textrm{d}x\right) \Delta u +V(x)u=|u|^{p-2}u~\hbox {in}~{\mathbb {R}}^N, u\in H^1({\mathbb {R}}^N),N\ge 1, \end{aligned}$$
where
$$M\in C([0,\infty ))$$
and
$$V\in C({\mathbb {R}}^N)$$
are given functions. Under very mild assumptions on M, we prove the existence of single-peak or multi-peak solution
$$u_\varepsilon $$
for above problem...
