A New Approach to Solving Singularly Perturbed NLS at Local Potential Maxima
Fuente:
arXiv
Guardado en:
| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911844067704832 |
|---|---|
| author | Zhang, Chengxiang |
| author_facet | Zhang, Chengxiang |
| contents | This paper presents a new approach for addressing the singularly perturbed nonlinear Schrödinger (NLS) equation:
\begin{equation}
-\varepsilon^2Δv + 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11362 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A New Approach to Solving Singularly Perturbed NLS at Local Potential Maxima Zhang, Chengxiang Analysis of PDEs 35J20, 35J15, 35J60 This paper presents a new approach for addressing the singularly perturbed nonlinear Schrödinger (NLS) equation: \begin{equation} -\varepsilon^2Δv + 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. |
| title | A New Approach to Solving Singularly Perturbed NLS at Local Potential Maxima |
| topic | Analysis of PDEs 35J20, 35J15, 35J60 |
| url | https://arxiv.org/abs/2404.11362 |