We study the Cauchy problem for the fractional Schrodinger equation iδtu = (m2 -Δ) α/2u + F(u) in R1+n, where n ≥1, m ≥ 0, 1 < α < 2, and F stands for the nonlinearity of Hartree type F(u)-λ(ψ(.)|•|-γ*|u|2)u with λ= ±1, 0 < γ < n, and 0 ≤ ψ ∈ L∞(Rn). We prove the existence and uniqueness of local and global solutions for certain α, γ, λ, ψ. We also remark on finite time blowup of solutions when λ =-1.
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