On a class of logarithmic Schrödinger equations via perturbation method
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913133203816448 |
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| author | Huang, Chen Yang, Zhipeng |
| author_facet | Huang, Chen Yang, Zhipeng |
| contents | In this paper, we consider the following logarithmic Schrödinger equation
\[
-Δu + V(x)u = u \log u^{2},\quad x\in\mathbb{R}^{N}.
\] Assuming that \(V\in C(\mathbb{R}^{N},\mathbb R)\), \(V\) is bounded away from zero, and \(V(x)\to+\infty\) as \(|x|\to\infty\), we develop a new perturbative variational approach to overcome the lack of \(C^{1}\)-smoothness of the associated functional and prove the existence and multiplicity of nontrivial weak solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12732 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On a class of logarithmic Schrödinger equations via perturbation method Huang, Chen Yang, Zhipeng Analysis of PDEs 35J60, 35J10 In this paper, we consider the following logarithmic Schrödinger equation \[ -Δu + V(x)u = u \log u^{2},\quad x\in\mathbb{R}^{N}. \] Assuming that \(V\in C(\mathbb{R}^{N},\mathbb R)\), \(V\) is bounded away from zero, and \(V(x)\to+\infty\) as \(|x|\to\infty\), we develop a new perturbative variational approach to overcome the lack of \(C^{1}\)-smoothness of the associated functional and prove the existence and multiplicity of nontrivial weak solutions. |
| title | On a class of logarithmic Schrödinger equations via perturbation method |
| topic | Analysis of PDEs 35J60, 35J10 |
| url | https://arxiv.org/abs/2601.12732 |