Normalized ground states for a kind of Choquard–Kirchhoff equations with critical nonlinearities

In this paper, we consider the existence of a normalized ground-state solution for the Choquard–Kirchhoff equation: $\{\begin{array}{lr}-(a+b{\int }_{{\mathbb{R}}^3}|\mathrm{\nabla }u{|}^{2}dx)\mathrm{\Delta }u=\lambda u+\mu (I_{\alpha }\ast |u{|}^p)|u{|}^{p-2}u+\omega |u{|}^{4}u,& \text{in}{\mathbb{R}}^3,\\ u>0,{\int }_{{\mathbb{R}}^3}|u{|}^2=m^2,& \text{in}{\mathbb{R}}^3,\end{array}$ \( \left \{ \textstyle\begin{array}{l@{\quad}r} -(a+b\int _{\mathbb{R}^{3}}|\nabla u|^{2}dx)\Delta{u}=\lambda u+\mu (I_{ \alpha}\ast |u|^{p})|u|^{p-2}u+\omega |u|^{4}u,\ \ &\text{in}\, \mathbb{R}^{3}, \\ u>0,\quad \int _{\mathbb{R}^{3}}|u|^{2}=m^{2},\,&\text{in}\, \mathbb{R}^{3}, \end{array}\displaystyle \right . \) where a, b, m, μ, $\omega >0$ $\omega >0$ , $p\in (2,\frac{7+\alpha }{3})$ $p\in (2,\frac{7+\alpha}{3})$ , $\lambda \in \mathbb{R}$ $\lambda \in \mathbb{R}$ , $\alpha \in (0,3)$ $\alpha \in (0,3)$ , and $I_{\alpha }$ $I_{\alpha}$ is a Riesz potential. Utilizing approximation methods and Schwartz symmetrization rearrangements, we establish the existence of normalized ground states for these kinds of mass-constrained Choquard–Kirchhoff problems.