关键词: 导数非线性Schrodinger系统, 含时势函数, 质量共振关系, 渐近行为

Abstract: We considered the initial  problem of  derivative  Schrodinger systems with time-dependent potentials and quadratic nonlinearities in high-dimensional （d≥3）space. Firstly, under the condition of mass resonance, we obtained the priori estimates of solutions to the systems by using the tools such as energy inequalities and embedding theorems. Secondly, we proved the global existence of solutions for the nonlinear Schrodinger systems with small initial value  by using priori estimates. Finally, by constructing auxiliary functions, we demonstrate that the solutions to the systems are asymptotically free under the condition of mass resonance.

Key words: derivative nonlinear Schrodinger system, time-dependent potential, mass resonance relation, asymptotic behavior