On the Landis Conjecture for Positive Quasi-linear Operators on Graphs
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916968160821248 |
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| author | Das, Ujjal Keller, Matthias Pinchover, Yehuda |
| author_facet | Das, Ujjal Keller, Matthias Pinchover, Yehuda |
| contents | We prove a Landis type unique continuation result for positive quasi-linear operators on graphs. Specifically, we give decay criteria that ensures when a harmonic function for a positive quasilinear Schrödinger operator with potential less than 1 is trivially zero. The assumption of positivity of the operator allows the application of criticality theory such as the Liouville comparison theorem. Furthermore, our results fundamentally build on the so called simplified energy. As an application we discuss the case of model graphs and in particular regular trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20559 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Landis Conjecture for Positive Quasi-linear Operators on Graphs Das, Ujjal Keller, Matthias Pinchover, Yehuda Analysis of PDEs We prove a Landis type unique continuation result for positive quasi-linear operators on graphs. Specifically, we give decay criteria that ensures when a harmonic function for a positive quasilinear Schrödinger operator with potential less than 1 is trivially zero. The assumption of positivity of the operator allows the application of criticality theory such as the Liouville comparison theorem. Furthermore, our results fundamentally build on the so called simplified energy. As an application we discuss the case of model graphs and in particular regular trees. |
| title | On the Landis Conjecture for Positive Quasi-linear Operators on Graphs |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.20559 |