Normalized solutions for a fractional $N/s$-Laplacian Choquard equation with exponential critical nonlinearities

Abstract

In this paper, we are concerned with the following fractional $N/s$-Laplacian Choquard equation \begin{align*} \begin{cases} (-\Delta)^s_{N/s}u=\lambda |u|^{\frac{N}{s}-2}u +(I_\mu*F(u))f(u),\ \ \mbox{in}\ \mathbb{R}^N, \displaystyle\int_{\mathbb{R}^N}|u|^{N/s} \mathrm{d}x=a^{N/s}, \end{cases} \end{align*} where $s\in(0,1)$, $1<\frac{N}{s}\in \mathbb{N}^+$, $a>0$ is a prescribed constant, $\lambda\in \mathbb{R}$, $I_\mu(x)=\frac{1}{|x|^{\mu}}$ with $\mu\in(0,N)$, $F$ is the primitive function of $f$, and $f$ is a continuous function with exponential critical growth of Trudinger-Moser type. Under some suitable assumptions on $f$, we prove that the above problem admits a ground state solution for any given $a>0$, by using the constraint variational method and minimax technique.