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- W2896565501 abstract "In 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<p¯ and the nonexistence of solution for the minimization problem infu∈Ds,2(RN)∖{0}{Jp,ϵ(u):⟨Jp,ϵ′(u),u⟩=0} for p=p¯, where Jp,ϵ(u)=∫R2Nϵ2s|u(x)−u(y)|2|x−y|N+2sdxdy+∫RNV|u|2−12p∫RN(Iα∗|u|p)|u|p. Inspired by the result, we further consider the existence and asymptotic behavior of groundstates for the above equation under a nonlocal perturbation, that is, equation ϵ2s(−Δ)su+V(x)u=(Iα∗|u|p)|u|p−2u+(Iα∗|u|q)|u|q−2uin RN with p_≤p<q≤p¯." @default.
- W2896565501 created "2018-10-26" @default.
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- W2896565501 date "2018-10-17" @default.
- W2896565501 modified "2023-10-17" @default.
- W2896565501 title "Semiclassical states for fractional Choquard equations with critical frequency" @default.
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- W2896565501 doi "https://doi.org/10.1080/17476933.2018.1530665" @default.
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