Multiple concentrating solutions for a fractional (p, q)-Choquard equation

We focus on the following fractional (p, q)-Choquard problem: (−Δ)psu+(−Δ)qsu+V(εx)(|u|p−2u+|u|q−2u)=1|x|μ*F(u)f(u) in RN,u∈Ws,p(RN)∩Ws,q(RN),u>0 in RN, $\begin{cases}{\left(-{\Delta}\right)}_{p}^{s}u+{\left(-{\Delta}\right)}_{q}^{s}u+V\left(\varepsilon x\right)\left(\vert u{\vert }^{p-2}u+\vert u{\vert }^{q-2}u\right)=\left(\frac{1}{\vert x{\vert }^{\mu }}{\ast}F\left(u\right)\right)f\left(u\right) \,\text{in}\,{\mathbb{R}}^{N},\quad \hfill \\ u\in {W}^{s,p}\left({\mathbb{R}}^{N}\right)\cap {W}^{s,q}\left({\mathbb{R}}^{N}\right), u{ >}0\,\text{in}\,{\mathbb{R}}^{N},\quad \hfill \end{cases}$ where ɛ > 0 is a small parameter, 0 < s < 1, 1