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Unbounded Solutions of the Stationary Schrödinger Equation on Riemannian Manifolds

Unbounded Solutions of the Stationary Schrödinger Equation on Riemannian Manifolds We study questions of existence and membership to a given functional class of unbounded solutions of the stationary Schrödinger equation Δu − cu = 0, where c is a smooth non-negative function on a non-compact Riemannian manifold M without boundary. We establish some interrelation between problems of existence of solutions of this equation on M and off some compact B ⊂ M with the same growth “at infinity”. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Unbounded Solutions of the Stationary Schrödinger Equation on Riemannian Manifolds

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Publisher
Springer Journals
Copyright
Copyright © Heldermann  Verlag 2003
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/bf03321048
Publisher site
See Article on Publisher Site

Abstract

We study questions of existence and membership to a given functional class of unbounded solutions of the stationary Schrödinger equation Δu − cu = 0, where c is a smooth non-negative function on a non-compact Riemannian manifold M without boundary. We establish some interrelation between problems of existence of solutions of this equation on M and off some compact B ⊂ M with the same growth “at infinity”.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 1, 2004

Keywords: Riemannian manifold; Schrödinger equation; 30F15; 31A05

References