Normalized solutions for a biharmonic Choquard equation with exponential critical growth in R4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^4$$\end{document}

In this paper, we study the following biharmonic Choquard-type problem Δ2u-βΔu=λu+(Iμ∗F(u))f(u),inR4,∫R4|u|2dx=c2>0,u∈H2(R4),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \begin{aligned} \left\{ \begin{array}{ll} \Delta ^2u-\beta \Delta u=\lambda u+(I_\mu *F(u))f(u), \quad \text{ in }\ \ \mathbb {R}^4,\\ \displaystyle \int \limits _{\mathbb {R}^4}|u|^2\textrm{d}x=c^2>0,\quad u\in H^2(\mathbb {R}^4), \end{array} \right. \end{aligned} \end{aligned}$$\end{document}where β≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta \ge 0$$\end{document}, λ∈R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda \in \mathbb {R}$$\end{document}, Iμ=1|x|μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_\mu =\frac{1}{|x|^\mu }$$\end{document} with μ∈(0,4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu \in (0,4)$$\end{document}, F(u) is the primitive function of f(u), and f is a continuous function with exponential critical growth. By using the mountain-pass argument, we prove the existence of radial ground-state solutions for the above problem.