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

We focus on the following fractional (p,q)-Choquard problem: {(-Delta)(p)(s)u + (-Delta)(q)(s)u + V(epsilon x)(vertical bar u vertical bar(p-2)u + vertical bar u vertical bar(q-2)u) = (1/vertical bar x vertical bar(mu)*F(u)) f(u) in R-N, u is an element of W-s,W-p(R-N) boolean AND W-s,W-q(R-N), u > 0 in R-N, where epsilon > 0 is a small parameter, 0 < s < 1, 1 < p < q < N/s, 0 < mu < sp,(-Delta)(r)(s), with r is an element of {p, q}, is the fractional r-Laplacian operator, V: R-N -> R is a positive continuous potential satisfying a local condition, f: R -> R is a continuous nonlinearity with subcritical growth at infinity and F(t) = integral(t)(0) f(tau)d tau. Applying suitable variationaland topological methods, we relate the number of solutions with the topology of the set where the potential V attains its minimum value.