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Optimal lower bounds for the spectrum of a second order linear differential equation with a p-integrable coefficient

Published online by Cambridge University Press:  14 November 2011

E. J. M. Veling
E. J. M. Veling
Affiliation:
Stichting Mathematisch Centrum, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands
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Synopsis

In this note the differential expression M[y] ≡ − y” + qy, q∈Lp(ℝ+) for some p ≧ l, is considered on [0,∞) together with the boundary condition either y(0) = 0 or y'(0) = 0. Lower bounds are given for the spectrum of the self-adjoint operators T generated by M[·] and these boundary conditions. The bounds depend on the Lp-norm of the coefficient q and they improve results of Everitt and Eastham. The bounds are optimal.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 92 , Issue 1-2 , 1982 , pp. 95 - 101
Copyright
Copyright © Royal Society of Edinburgh 1982

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References

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