Bounded solutions of the Schrödinger equation on Riemannian products (Q2780508)
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scientific article; zbMATH DE number 1729115
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bounded solutions of the Schrödinger equation on Riemannian products |
scientific article; zbMATH DE number 1729115 |
Statements
5 August 2002
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Dirichlet problem on a manifold
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harmonic functions on a manifold
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Schrödinger equation
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Liouville theorem
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Bounded solutions of the Schrödinger equation on Riemannian products (English)
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Using the authors' abstract: The stationary Schrödinger equation \(\Delta n-c(x)n= 0\) is considered on complete Riemannian manifolds \(M\) of specific type. For this equation the behaviour of the bounded solutions is studied. Sufficient conditions for solvability are obtained for some boundary-value problems, including a condition equivalent to the stability of the Dirichlet problem for the above equations on \(M\). Also conditions are found under which the Liouville theorem holds.
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