奇异势非齐次非线性schrÖdinger方程的轨道稳定性

IF 0.5 4区数学 Q3 MATHEMATICS

Bulletin of the Korean Mathematical Society Pub Date : 2019-01-01 DOI:10.4134/BKMS.B190029

Yonggeun Cho, Misung Lee

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引用次数: 6

摘要

我们证明了具有奇异线性势和本质上是质量亚临界功率型非线性的非线性Schrödinger方程的基态和驻波轨道稳定性的存在性。为此，我们建立了H1中基态的存在性。我们不假设对称或单调。我们还考虑了能量次临界方程的Strichartz解的局部和全局适定性。在三维空间中，我们略微提高了[5,12]中的非齐次系数的取值范围。

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ON THE ORBITAL STABILITY OF INHOMOGENEOUS NONLINEAR SCHRÖDINGER EQUATIONS WITH SINGULAR POTENTIAL

We show the existence of ground state and orbital stability of standing waves of nonlinear Schrödinger equations with singular linear potential and essentially mass-subcritical power type nonlinearity. For this purpose we establish the existence of ground state in H1. We do not assume symmetry or monotonicity. We also consider local and global well-posedness of Strichartz solutions of energy-subcritical equations. We improve the range of inhomogeneous coefficient in [5, 12] slightly in 3 dimensions.

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来源期刊

Bulletin of the Korean Mathematical Society 数学-数学

CiteScore

0.80

自引率

20.00%

发文量

审稿时长

6 months

期刊介绍： This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).