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• W2034865045 abstract "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 $$Omegasubseteq mathbb{R}^d$$ such that P 1 is critical in Ω with a ground state φ, the function $$psinleq 0$$ is a subsolution of the equation P 0 u = 0 in Ω and satisfies $$psi_+leq Cvarphi$$ in Ω, then P 0 is critical in Ω and $$psi$$ is its ground state. In particular, $$psi$$ is (up to a multiplicative constant) the unique positive supersolution of the equation P 0 u = 0 in Ω. Similar results hold for general symmetric operators, and also on Riemannian manifolds." @default.
• W2034865045 created "2016-06-24" @default.
• W2034865045 creator A5016714048 @default.
• W2034865045 date "2007-03-02" @default.
• W2034865045 modified "2023-09-23" @default.
• W2034865045 title "A Liouville-type Theorem for Schrödinger Operators" @default.
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• W2034865045 doi "https://doi.org/10.1007/s00220-007-0197-3" @default.
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