Solutions for a Fractional Kirchhoff–Choquard Equation

In this paper, we mainly study the fractional elliptic equation: $$\left(a+b\int\limits_{\mathbb{R}^{3}}|(-\Delta)^{\frac{s}{2}}u|^{2}dx\right)(-\Delta)^{s}u+u=(|x|^{-\mu}*|u|^{p})|u|^{p-2}u,\quad x\in\mathbb{R}^{3},$$ where $$\mu\in(0,3)$$ , $$s\in(0,1)$$ , $$2-\frac{\mu}{3} 0$$ . For this equation, we will discuss it in two case. For $$s\in(0,\frac{3}{4}]$$ , we prove the existence of solutions by establishing an equivalent system. For $$s\in(\frac{3}{4},1)$$ , we use the symmetric mountain pass lemma to prove that the equation has infinitely many solutions.