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• W2017625993 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 $P_j:=-Delta+V_j$, for $j=0,1$, are two nonnegative Schrodinger operators defined on $Omegasubseteq mathbb{R}^d$ such that $P_1$ is critical in $Omega$ with a ground state $phi$, the function $psinleq 0$ is a subsolution of the equation $P_0u=0$ in $Omega$ and satisfies $|psi|leq Cphi$ in $Omega$, then $P_0$ is critical in $Omega$ and $psi$ is its ground state. In particular, $psi$ is (up to a multiplicative constant) the unique positive supersolution of the equation $P_0u=0$ in $Omega$. Similar results hold for general symmetric operators, and also on Riemannian manifolds." @default.
• W2017625993 created "2016-06-24" @default.
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• W2017625993 date "2005-12-18" @default.
• W2017625993 modified "2023-09-27" @default.
• W2017625993 title "A Liouville-type theorem for Schrodinger operators" @default.
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