In this paper, we consider the following Choquard equation: $\begin{array}{r}-\mathrm{\Delta }u+u=(I_{\alpha }\ast F(u\left)\right)F^{\prime }\left(u\right)\mathrm{i}\mathrm{n}{\mathbb{R}}^N\end{array}$ where $N⩾3$, $\alpha \in (0,N)$, $I_{\alpha }$ is the Riesz potential, and $F\left(u\right):=\frac{1}{p}|u{|}^p+\frac{1}{q}|u{|}^q$, where $p=\frac{N+\alpha }{N}$ and $q=\frac{N+\alpha }{N-2}$ are lower and upper critical exponents in sense of the Hardy–Littlewood–Sobolev inequality. Based on perturbation method and the invariant sets of descending flow, we prove that the above equation possesses infinitely many sign-changing solutions. Our results extend the results in Seok [Nonlinear Choquard equations: doubly critical case. Appl Math Lett. 2018;76:148–156] and Su [New result for nonlinear Choquard equations: doubly critical case. Appl Math Lett. 2020;102(106092):0–7].

在本文中，我们考虑以下 Choquard 方程：$\begin{array}{r}-\mathrm{\Delta }你+你=({\mathrm{一世}}_{\alpha }*F(你\left)\right)F^{\text{'}}\left(你\right)\mathrm{一世}\mathrm{n}{\mathbb{R}}^{ñ}\end{array}$在哪里$ñ⩾3$,$\alpha \in (0,ñ)$,${\mathrm{一世}}_{\alpha }$是 Riesz 势，并且$F\left(你\right):=\frac{1}{p}|你{|}^p+\frac{1}{q}|你{|}^q$， 在哪里$p=\frac{ñ+\alpha }{ñ}$和$q=\frac{ñ+\alpha }{ñ-2}$是 Hardy-Littlewood-Sobolev 不等式意义上的下临界指数和上临界指数。基于摄动法和下行流的不变集，我们证明了上述方程具有无穷多个变号解。我们的结果扩展了 Seok [非线性 Choquard 方程：双重临界情况。应用数学莱特。2018;76:148–156] 和 Su [非线性 Choquard 方程的新结果：双重临界情况。应用数学莱特。2020；102（106092）：0-7]。