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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.14491 |
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| _version_ | 1866914838692757504 |
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| author | Filonov, N. D. Krymskii, S. T. |
| author_facet | Filonov, N. D. Krymskii, S. T. |
| contents | The equation $- Δu + V u = 0$ in the cylinder $\mathbb{R} \times (0,2π)^d$ with periodic boundary conditions is considered. The potential $V$ is assumed to be bounded, and both functions $u$ and $V$ are assumed to be real-valued. It is shown that the fastest rate of decay at infinity of non-trivial solution $u$ is $O\left(e^{-c|w|}\right)$ for $d=1$ or $2$, and $O\left(e^{-c|w|^{4/3}}\right)$ for $d\ge 3$. Here $w$ is the axial variable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_14491 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Landis conjecture in a cylinder Filonov, N. D. Krymskii, S. T. Analysis of PDEs 35J10, 35B40 The equation $- Δu + V u = 0$ in the cylinder $\mathbb{R} \times (0,2π)^d$ with periodic boundary conditions is considered. The potential $V$ is assumed to be bounded, and both functions $u$ and $V$ are assumed to be real-valued. It is shown that the fastest rate of decay at infinity of non-trivial solution $u$ is $O\left(e^{-c|w|}\right)$ for $d=1$ or $2$, and $O\left(e^{-c|w|^{4/3}}\right)$ for $d\ge 3$. Here $w$ is the axial variable. |
| title | On the Landis conjecture in a cylinder |
| topic | Analysis of PDEs 35J10, 35B40 |
| url | https://arxiv.org/abs/2311.14491 |