Computational Methods and Function Theory 3 (2003), No. 2, 443--451
Copyright Heldermann Verlag 2003
Alexander G. Losev
alexander.losev@volsu.ru , Department of Mathematical Analysis and Function Theory, Volgograd State University, Vtoraya Prodol'naya ul. 30, 400062 Volgograd, Russia.
Elena A. Mazepa
lmazepa@rambler.ru , Department of Mathematical Analysis and Function Theory, Volgograd State University, Vtoraya Prodol'naya ul. 30, 400062 Volgograd, Russia.
Victoriya Y. Chebanenko
vchebanenko@rambler.ru , Department of Mathematical Analysis and Function Theory, Volgograd State University, Vtoraya Prodol'naya ul. 30, 400062 Volgograd, Russia.
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 subset B of M with the same growth "at infinity''.
Keywords: Riemannian manifold, Schrödinger equation.
MSC 2000: Primary 30F15; Secondary 31A05.
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