Existence and concentration of ground-states for fractional Choquard equation with indefinite potential

Abstract This paper is concerned with existence and concentration properties of ground-state solutions to the following fractional Choquard equation with indefinite potential: (− Δ) s u + V (x) u = ∫ R N A (ε y) ∣ u (y) ∣ p ∣ x − y ∣ μ d y A (ε x) ∣ u (x) ∣ p − 2 u (x), x ∈ R N, (-) ^su+V (x) u= ({ₑ^N}A (y) | u (y) | ^{p}| x-y{| ^ }dy) A (x) | u (x) | ^p-2u (x), 1emx {R}^N, where s ∈ (0, 1) s (0, 1), N > 2 s N 2s, 0 μ 2 s 0 2s, <jats: inline-graphic xmlns: xlink="http: //www. w3