论文标题
非线性schrödinger方程的最终状态问题，带有时间偿还的谐波振荡器
Final state problem for nonlinear Schrödinger equations with time-decaying harmonic oscillators
论文作者
论文摘要
我们考虑具有合适时间偿还的谐波振荡器的非线性Schrödinger方程（NLS）的最终问题。在此方程式中，如果$ 0 <ρ\ leq 2/（n（1-λ））$，则在远程类中包含非线性$ | u |^ρu$的功率，其功率由$ 0 \leqλ<1/2 $，由谐波电位和laplacian系数确定。在本文中，我们找到了该系统的最终状态，并获得了渐近学的衰减估计。
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|^ρu $ is included in the long-range class if $0 < ρ\leq 2/(n(1- λ)) $ with $0 \leq λ<1/2$, 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.
