Partially APN functions attract researchers' particular interest recently. It plays an important role in studying APN functions. In this paper, based on the multivariate method and resultant elimination, we propose several new infinite classes of $0$-APN power functions over $\mathbb{F}_{2^n}$. Furthermore, two infinite classes of $0$-APN power functions $x^d$ over $\mathbb{F}_{2^n}$ are characterized completely where $(2^k-1)d\equiv 2^m-1~({\rm mod}\ 2^n-1)$ or $(2^k+1)d\equiv 2^m+1~({\rm mod}\ 2^n-1)$ for some positive integers $n, m, k$. These infinite classes of $0$-APN power functions can explain some examples of exponents of Table $1$ in \cite{BKRS2020}.

翻译：APN 功能最近部分吸引了研究人员的特殊兴趣。 它在研究APN 函数方面起着重要作用 。 在本文中, 基于多变方法并随之消除, 我们提议在$\mathbb{F\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\