Standing waves to upper critical Choquard equation with a local perturbation: Multiplicity, qualitative properties and stability

Abstract In this article, we consider the upper critical Choquard equation with a local perturbation − Δ u = λ u + (I α ∗ ∣ u ∣ p) ∣ u ∣ p − 2 u + μ ∣ u ∣ q − 2 u, x ∈ R N, u ∈ H 1 (R N), ∫ R N ∣ u ∣ 2 = a, \array{l- u= u+ (I | u-0. 25em| ^p) | u-0. 25em| ^p-2u+ | u-0. 25em| ^q-2u, 1emx {R}^N, \\ u H^1 ({R}^N), 1em {ₑ^N}| u-0. 25em| ^2=a, array. where N ≥ 3 N 3, μ > 0 0