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arXiv · 2404.11362

A New Approach to Solving Singularly Perturbed NLS at Local Potential Maxima

Chengxiang Zhang
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Abstract

This paper presents a new approach for addressing the singularly perturbed nonlinear Schr\"odinger (NLS) equation: \begin{equation} -\varepsilon^2\Delta v + V(x) v =f(v),\ v>0,\ \lim_{|x|\to \infty} v(x)=0, \end{equation} where $V$ possesses a local maximum point and $f$ satisfies the Berestycki-Lions conditions.The key to our approach is the derivation of a refined lower bound on the gradient norm.

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Chengxiang Zhang. 2024-04-17. A New Approach to Solving Singularly Perturbed NLS at Local Potential Maxima. https://arxiv.org/abs/2404.11362

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