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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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Table of 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.