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arXiv · 1812.06738

Orbital stability of standing waves for Schr\"{o}dinger type equations with slowly decaying linear potential

Xinfu Li·Junying Zhao
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Abstract

In this paper, kinds of Schr\"{o}dinger type equations with slowly decaying linear potential and power type or convolution type nonlinearities are considered. By using the concentration compactness principle, the sharp Gagliardo-Nirenberg inequality and a refined estimate of the linear operator, the existence and orbital stability of standing waves in $L^2$-subcritical and $L^2$-critical cases are established in a systematic way.

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Xinfu Li, Junying Zhao. 2018-12-17. Orbital stability of standing waves for Schr\"{o}dinger type equations with slowly decaying linear potential. https://arxiv.org/abs/1812.06738

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