The Landis conjecture via Liouville comparison principle and criticality theory
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909207093051392 |
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| author | Das, Ujjal Pinchover, Yehuda |
| author_facet | Das, Ujjal Pinchover, Yehuda |
| contents | We give partial affirmative answers to Landis conjecture in all dimensions for two different types of linear, second order, elliptic operators in a domain $Ω\subset \mathbb{R}^N$. In particular, we provide a sharp decay criterion that ensures when a solution of a nonnegative Schrödinger equation in $\mathbb{R}^N$ with a potential $V\leq 1$ is trivial. Moreover, we address the analogue of Landis conjecture for quasilinear problems. Our approach relies on the application of Liouville comparison principles and criticality theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11695 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Landis conjecture via Liouville comparison principle and criticality theory Das, Ujjal Pinchover, Yehuda Analysis of PDEs Mathematical Physics Classical Analysis and ODEs Functional Analysis Spectral Theory 35J10, 35B09, 35B53, 35B60 We give partial affirmative answers to Landis conjecture in all dimensions for two different types of linear, second order, elliptic operators in a domain $Ω\subset \mathbb{R}^N$. In particular, we provide a sharp decay criterion that ensures when a solution of a nonnegative Schrödinger equation in $\mathbb{R}^N$ with a potential $V\leq 1$ is trivial. Moreover, we address the analogue of Landis conjecture for quasilinear problems. Our approach relies on the application of Liouville comparison principles and criticality theory. |
| title | The Landis conjecture via Liouville comparison principle and criticality theory |
| topic | Analysis of PDEs Mathematical Physics Classical Analysis and ODEs Functional Analysis Spectral Theory 35J10, 35B09, 35B53, 35B60 |
| url | https://arxiv.org/abs/2405.11695 |