In this paper, we consider the normalized ground state solution 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 ground state normalized solution.
Categories: math.AP