Let $k$ be a perfect field of characteristic $p>0$ and $W:=W(k)$ is the witt ring. Let $K$ be a totally ramified extension of $K_0:=W(\frac{1}{p})$ and $\Lambda:=W[[u]]$ is the formal series ring in the inderminate $u$.

Due to Brueil and Kisin, there is an exact functor between the categories $BT^\phi_{/\Lambda}$ and $BT(O_K)$, $BT(O_K)$ is the category of p-divisible groups over $O_K$(i.e. every $G_n$ is a group scheme over $O_K$) and $BT^\phi_{/\Lambda}$ is the category of finite free $\Lambda$ module $A$ equipped with an injective semi-linear map $\phi: A\rightarrow A$ satisfying some conditions. 

When $p>2$, this is an equivance of categroies and when $p=2$, this is an equivance up to isogeny.

Question: What is the motivation of classifying $p$-divisible groups? Does it have some applications on p-adic Hodge theory?

Thanks!