Abstract This paper focuses on the study of multiplicity and localized concentration properties of positive solutions for the following singularly perturbed double phase problem with nonlocal Choquard reaction aligned \ array{ll - ^p u- ^q ₐ u +V (x) (|u|^p-2u+|u|^q-2u) \\ = ^ -N (1|x|^{ }*G (u) ) g (u), & in~ R^N, \\ u W^1, p (R^N) W^1, q (R^N), u>0, & in~ R^N, \\ array. aligned - ϵ p Δ p u - ϵ q Δ q u + V (x) (| u | p - 2 u + | u | q - 2 u) = ϵ μ - N 1 | x | μ ∗ G (u) g (u), in R N, u ∈ W 1, p (R
Zhang et al. (2026) studied this question.