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We consider the following Cauchy problem: -iut=Δu-V(x)u+f(x,|u|2)u+(W(x)⋆|u|2)u, x∈ℝN,t>0, u(x, 0)=u0(x),x∈ℝN, where V(x) and W(x) are real-valued potentials and V(x)≥0 and W(x) is even, f(x,|u|2) is measurable in x and continuous in |u|2, and u0(x) is a complex-valued function of x. We obtain some sufficient conditions and establish two sharp thresholds for the blowup and global existence of the solution to the problem

Phenomena of Blowup and Global Existence of the Solution to a Nonlinear Schrödinger Equation