Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35J10, 35P99, 47A40

Retrieve articles in all journals with MSC: 35J10, 35P99, 47A40


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0536943-1
PII: S 0002-9947(1979)0536943-1
Article copyright: © Copyright 1979 American Mathematical Society