Multiple nodal solutions of nonlinear Choquard equations

In this paper, we consider the existence of multiple nodal solutions of the nonlinear Choquard equation \begin{equation*} \ \ \ \ (P)\ \ \ \ \begin{cases} -\Delta u+u=(|x|^{-1}\ast|u|^p)|u|^{p-2}u \ \ \ $\text{in}$\ $\mathbb{R}$^3, \ \
\ \ u\in H^1($\mathbb{R}$^3),\ \end{cases} \end{equation*} where $p\in (\frac{5}{2},5)$\mathrm{.}Weshowthatforanypositiveinteger$k$,problem$(P)$ has at least a radially symmetrical solution changing sign exactly $k$-times.