Concentrating solutions of the fractional $(p,q)$-Choquard equation with exponential growthSong, Yueqiang (Avtor) Sun, Xueqi (Avtor) Repovš, Dušan (Avtor) fractional double phase operatorcritical exponential growthmountain pass theoremTrudinger–Moser inequalityvariational methodThis paper deals with the following fractional $(p,q)$-Choquard equation with exponential growth of the form: $\varepsilon^{p s} (-\Delta)^{s}_{p} u + \varepsilon^{q s} (-\Delta)^{s}_{q} u + Z(x) ( |u|^{p-2} u + |u|^{q-2} u)$ $=\varepsilon^{\mu - N} [ |x|^{-\mu} * F(u) ] f(u)$ in $\mathbb{R}^N,$ where $s \in (0,1)$, $\varepsilon > 0$ is a parameter, $2 \leq p = \frac{N}{s} < q$, and $0 < \mu < N$. The nonlinear function $f$ has exponential growth at infinity, and the continuous potential function $Z$ satisfies suitable natural conditions. Using Ljusternik–Schnirelmann category theory and variational methods, the multiplicity and concentration of positive solutions are obtained for $\varepsilon > 0$ small enough. In a certain sense, we generalize some previously known results.20262026-03-09 09:53:40Neznano28044sl