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} (-Δ)^s_{N/s}u=λ|u|^{\frac{N}{s}-2}u +(I_μ*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.