On Landis’ conjecture in the plane when the potential has an exponentially decaying negative part. (English) Zbl 1439.35109
St. Petersbg. Math. J. 31, No. 2, 337-353 (2020) and Algebra Anal. 31, No. 2, 204-226 (2019).
The authors consider equations of the form
\(-\Delta u+Vu=0\) in \(\mathbb{R}^2\), where \(V=V_+-V_-\), \(V_+\in L^{\infty}\), and \(V_-\) is a nontrivial function that exhibits exponential decay at infinity. By some new ides and methods, they get a quantitative version of Landis’ conjecture.
Reviewer: Zhipeng Yang (Göttingen)
MSC:
| 35B60 | Continuation and prolongation of solutions to PDEs |
| 35J10 | Schrödinger operator, Schrödinger equation |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35B45 | A priori estimates in context of PDEs |
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