On the Landis conjecture in a cylinder
| Autor: | Filonov, N. D., Krymskii, S. T. |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The equation $- \Delta u + V u = 0$ in the cylinder $\mathbb{R} \times (0,2\pi)^d$ 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. Comment: In the first version of the paper we constructed a real example for the Landis conjecture in the half-cylinder. Now, we constructed an example in the whole cylinder |
| Databáze: | arXiv |
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