Semiclassical states for fractional Choquard equations with critical frequency

ABSTRACTIn this paper, we study the semiclassical states for the fractional Choquard equation ϵ2s(−Δ)su+V(x)u=(Iα∗|u|p)|u|p−2uin RN, where s∈(0,1), N>2s, (N+α)/N=p_≤p≤p¯=(N+α)/(N−2s), α∈(0,N) and Iα=1/|x|N−α, V(x) is a continuous potential satisfying suitable assumptions and ϵ>0 is a small parameter. Using the mountain pass lemma and the Brezis-Lieb lemma, we prove the existence and asymptotic behavior of groundstates for p_≤p

Keywords:

• Mathematical analysis
• Mathematics
• Semiclassical physics
• Critical frequency
• Quantum mechanics
• minimization problem
• Lemma (mathematics)
• Asymptotic analysis
• Mathematical physics

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