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In this article, we study the following fractional critical Schrödinger system
(−Δ)sui = μiu3i+ βuiΣj≠i u2j+ λiui in Ω,
ui = 0 on RN \ Ω, i = 1, 2, · · · , m,
where 0 < s < 1, μi > 0, coupling constant β satisfies either −∞ < β ≤ ¯ β ( ¯ β > 0 small) or β → −∞,0 < λi < λs1(Ω), where λs1(Ω) is the first eigenvalue of (−Δ)s on Ω, with Ω is a smooth bounded domain in RN with N = 4s. Under some geometric assumptions on Ω, we construct solutions which concentrate and blow up at different points as λ1, · · · , λm → 0.
2020 Mathematics Subject Classification: Primary 35R11, 35J60; Secondly 47G20.