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Saddle solutions for the fractional Choquard equation

We study the saddle solutions for the fractional Choquard equation \begin{align*} (-Δ)^{s}u+ u=(K_α\ast|u|^{p})|u|^{p-2}u, \quad x\in \mathbb{R}^N \end{align*} where $s\in(0,1)$, $N\geq 3$ and $K_α$ is the Riesz potential with order $α\in (0,N)$. For every Coxeter group $G$ with rank $1\leq k\leq N$ and $p\in[2,\frac{N+α}{N-2s})$, we construct a $G$-saddle solution with prescribed symmetric nodal configurations. This is a counterpart for the fractional Choquard equation of saddle solutions to the Choquard equation and further completes the existence of non-radial sign-changing solutions for this doubly nonlocal equation.