一类带调和势具非齐次项的非线性Schrödinger方程

摘要

The inhomogeneous nonlinear Schrödinger equation with harmonic potential is discussed.By es-tablishing the corresponding energy function and the variational structure and through applying the po-tential well argument,the concave function and the improved Gagliardo-Nirenberg interpolation in-equation,the optimum conditions for the global solution and explosive solution for the Cauchy problem are obtained.In addition,the initial value for the existence of global solution is determined.%讨论一类带调和势的具有非齐次项的非线性 Schrödinger方程初值问题。通过构造对应的能量泛函、变分结构，运用势井方法、凹函数和改进过的 Gagliardo-Nirenberg插值不等式，得到 Cauchy问题整体解及爆破解存在的最佳条件，并且证明了整体解存在的初值具体取值范围。