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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


On the positive spectrum of Schrödinger operators with long range potentials

Authors: G. B. Khosrovshahi, H. A. Levine and L. E. Payne
Journal: Trans. Amer. Math. Soc. 253 (1979), 211-228
MSC: Primary 35J10; Secondary 35P99, 47A40
MathSciNet review: 536943
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Abstract: In this paper we are concerned with solutions of the equation $ \Delta u\, + \,p(x)u\, = \,0$ in an unbounded domain $ \Omega $ in $ {R^n}$, $ \Omega \, \supset \,\{ x\vert\,\,\left\Vert x \right\Vert\, \geqslant \,{R_0}\} $. The main result is a determination of conditions on the asymptotic behavior of $ p(x)$ sufficient to guarantee that no nontrivial $ {L_2}$ solution exists. Our results contain those of previous authors as special cases. The principal application is to the determination of upper bounds for positive eigenvalues of Schrödinger operators.

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PII: S 0002-9947(1979)0536943-1
Article copyright: © Copyright 1979 American Mathematical Society