Normalized ground states for a biharmonic Choquard equation with exponential critical growth

Abstract In this paper, we consider the normalized ground state solutions for the following biharmonic Choquard type problem \begin{align*}\begin{split}\left\{\begin{array}{ll}\Delta^2u-\beta\Delta u=\lambda u+(I_\mu*F(u))f(u),\quad\mbox{in}\ \ \mathbb{R}^4, \\\displaystyle\int_{\mathbb{R}^4}|u|^2dx=c^2,\quad u\in H^2(\mathbb{R}^4),\\\end{array}\right.\end{split}\end{align*} where $\beta\geq0$ , c > 0, $\lambda\in \mathbb{R}$ , $I_\mu=\frac{1}{|x|^\mu}$ with $\mu\in (0,4)$ , F ( u ) is the primitive function of f ( u ), and f is a continuous function with exponential critical growth in the sense of the Adams inequality. By using a minimax principle based on the homotopy stable family, we obtain that the above problem admits at least one normalized ground state solution.