We consider the final-state problem for the nonlinear Schrödinger equations (NLS) with a suitable time-decaying harmonic oscillator. In this equation, the power of nonlinearity $|u{|}^{\rho }u$ is included in the long-range class if $0<\rho \le 2/(n(1-\lambda ))$ with $0\le \lambda <1/2$, which is determined by the harmonic potential and a coefficient of Laplacian. In this paper, we find the final state for this system and obtain the decay estimate for asymptotics.

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具时间衰减谐波振荡器的非线性Schrödinger方程的最终状态问题

我们考虑了带有合适的时衰减谐波振荡器的非线性Schrödinger方程（NLS）的最终状态问题。在这个方程中，非线性的力量$|ü{|}^{\rho }ü$ 包括在远程课程中，如果 $0<\rho \le \mathrm{2个}/（ñ（\mathrm{1个}-\lambda ））$ 和 $0\le \lambda <\mathrm{1个}/\mathrm{2个}$，这取决于谐波电位和拉普拉斯系数。在本文中，我们找到了该系统的最终状态，并获得了渐近线的衰减估计。