A Liouville-type theorem for Schrödinger operators
| dc.creator | Pinchover, Yehuda | |
| dc.date | 2005-12-18 | |
| dc.date | 2006-01-16 | |
| dc.date.accessioned | 2026-07-07T06:55:29Z | |
| dc.date.available | 2026-07-07T06:55:29Z | |
| dc.description | In this paper we prove a sufficient condition, in terms of the behavior of a ground state of a symmetric critical operator $P_1$, such that a nonzero subsolution of a symmetric nonnegative operator $P_0$ is a ground state. Particularly, if $P_j:=-Δ+V_j$, for $j=0,1$, are two nonnegative Schrödinger operators defined on $Ω\subseteq \mathbb{R}^d$ such that $P_1$ is critical in $Ω$ with a ground state $ϕ$, the function $ψ\nleq 0$ is a subsolution of the equation $P_0u=0$ in $Ω$ and satisfies $|ψ|\leq Cϕ$ in $Ω$, then $P_0$ is critical in $Ω$ and $ψ$ is its ground state. In particular, $ψ$ is (up to a multiplicative constant) the unique positive supersolution of the equation $P_0u=0$ in $Ω$. Similar results hold for general symmetric operators, and also on Riemannian manifolds. | |
| dc.description | 14 pages, the main result was improved, and a few more applications were added | |
| dc.identifier | https://arxiv.org/abs/math/0512431 | |
| dc.identifier | http://arxiv.org/abs/math/0512431 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/106296 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Spectral Theory | |
| dc.subject | 35J150; 35B05 | |
| dc.title | A Liouville-type theorem for Schrödinger operators | |
| dc.type | text |