A New Approach to Solving Singularly Perturbed NLS at Local Potential Maxima
Analysis of PDEs
2024-04-18 v1
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 possesses a local maximum point and satisfies the Berestycki-Lions conditions.The key to our approach is the derivation of a refined lower bound on the gradient norm.
Cite
@article{arxiv.2404.11362,
title = {A New Approach to Solving Singularly Perturbed NLS at Local Potential Maxima},
author = {Chengxiang Zhang},
journal= {arXiv preprint arXiv:2404.11362},
year = {2024}
}