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Lower bounds for the spectrum of a second order linear differential equation with a coefficient whose negative part is p-integrable

Published online by Cambridge University Press:  14 November 2011

B. J. Harris
B. J. Harris
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, Dekalb, Illinois 60115, U.S.A.
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Synopsis

We consider ihe differential expression M[y]: = −y″ + qy on [0, ∞) where q_∈ Lp [0, ∞) for some p ≧ 1. It is known that M, together with the boundary conditions y(0) = 0 or y′(0) = 0, defines linear operators on L2 [0, ∞). We obtain lower bounds for the spectra of these operators. Our bounds depend on the Lp norm of q_ and extend results of Everitt and Veling.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 97 , 1984 , pp. 105 - 107
Copyright
Copyright © Royal Society of Edinburgh 1984

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References

1Everitt, W. N.. On the spectrum of a second order linear differential equation with a p-integrable coefficient. Applicable Anal. 2 (1972), 143–160.CrossRefGoogle Scholar
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3Nagy, Béla V. Sz. Über Integralungleichungen zwischen einer Funktion und ihrer Ableitung. Acta Sci. Math. (Szeged) 10 (1941), 64–74.Google Scholar
4Veling, E. J. M.. Optimal lower bounds for the spectrum of a second order linear differential equation with a p-integrable coefficient. Proc. Roy. Soc. Edinburgh Sect. A 92 (1982), 95–101.CrossRefGoogle Scholar