Existence of solutions for a fractional Choquard--type equation in $\mathbb{R}$ with critical exponential growth

Rodrigo Clemente, José Carlos de Albuquerque, Eudes Barboza

In this paper we study the following class of fractional Choquard--type equations \[ (-Δ)^{1/2}u + u=\Big( I_μ\ast F(u)\Big)f(u), \quad x\in\mathbb{R}, \] where $(-\Delta {)}^{1/2}$ denote…