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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
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
References
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