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Oscillation criteria of Nehari-type for Sturm–Liouville operators and elliptic differential operators of second order and the lower spectrum

Published online by Cambridge University Press:  14 November 2011

F. Fiedler
F. Fiedler
Affiliation:
Sektion Mathematik/Physik, Pädogogische Hochschule “Dr. Theodor Neubauer”, Erfurt, DDR 5010, German Democratic Republic
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Synopsis

Sufficient oscillation criteria of Nehari-type are established for the differential equation −uʺ(t) + q(t)u(t) = 0, 0<t<∞, with and without sign restrictions on q(t), respectively. These results are extended to Sturm-Liouville equations and elliptic differential equations of second order.In Section 7 we present conclusions for the lower spectrum of elliptic differential operators and also for the discreteness of the spectrum of certain ordinary differential operators of second order.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 109 , Issue 1-2 , 1988 , pp. 127 - 144
Copyright
Copyright © Royal Society of Edinburgh 1988

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