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

We focus on the following fractional (p, q)-Choquard problem: (Formula Presented) where ε > 0 is a small parameter, 0 < s < 1, 1 < p < q < Ns , 0 < μ < sp, (−Δ)sr, with r ∈ {p, q}, is the fractional r-Laplacian operator, V: ℝN → 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) = ∫0t f(τ) dτ. Applying suitable variational and topological methods, we relate the number of solutions with the topology of the set where the potential V attains its minimum value.