In this paper, we study the following fractional Choquard-type equation with prescribed mass \begin{ align*} \begin{ cases} (-\Delta)^{ 1/2}u=\lambda u +(I_\mu*F(u))f(u),\ \ \mbox{ in}\ \mathbb{ R}, \displaystyle\int_{ \mathbb{ R}}|u|^2 \mathrm{ d}x=a^2, \end{ cases} \end{ align*} where $(-\Delta)^{ 1/2}$ denotes the $1/2$-Laplacian operator, $a>0$, $\lambda\in \mathbb{ R}$, $I_\mu(x)=\frac{ { 1}}{ { |x|^\mu}}$ with $\mu\in(0,1)$, $F(u)$ is the primitive function of $f(u)$, and $f$ is a continuous function with exponential critical growth in the sense of the Trudinger-Moser inequality. By using a minimax principle based on the homotopy stable family, we obtain that there is at least one normalized ground state solution to the above equation.
Categories: math.AP