中文摘要：

该文在R^3中研究如下Schrodinger-Hartree方程i tψ＋△ψ=-（｜x｜^-1＊｜ψ｜^α）｜ψ｜^α-2ψ,t〉0,x∈R^3,α≥2.（P）利用Gagliardo-Nirenberg与方程（P）的质量守恒律,能量守恒律建立方程的发展不变流.以此为基础在7/3≤α〈5时,得到其Cauchy问题的爆破解和整体解的门槛条件.

英文摘要：

In this paper, the Schrodinger-Hartree equation i tψ＋△ψ=-（｜x｜^-1＊｜ψ｜^α）｜ψ｜^α-2ψ,t〉0,x∈R^3,α≥2.（P） is considered in R^3. We establish invariant evolution flows of the equation by Gagliardo- Nirenberg inequality, mass conservation and energy conservation of the equation （P）. When 7/3≤α〈5 a sharp threshold of global existence and blow-up of the Cauthy problem is derived.