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On the location of spectral concentration for perturbed discrete spectra

Part of: Ordinary differential operators

Published online by Cambridge University Press:  26 February 2010

M. S. P. Eastham
M. S. P. Eastham
Affiliation:
Department of Computer Science, Cardiff University of Wales, P.O. Box 916, Cardiff CF24 3XF
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Extract

We consider the spectral function

associated with the Sturm-Liouville equation

in situations where q(x) →−∞ as x → ∞ and (1.1) is in the Weyl limit-point case at ∞. As usual, q is real-valued and locally integrable in [0, ∞], and our particular concern is where q(x) has the form

where c (>0) is a parameter, s and p are non-negative on [0, ∞], p(x) → ∞ and p(x) = 0{s(x) } as x → ∞. As the boundary condition at x = 0, we take the Dirichlet condition y(0) = 0 for convenience: we can equally take the Neumann condition y′ (0) = 0 or generally a1y(0) + a2y′ (0) = 0 with real a1 and a2.

MSC classification

Secondary: 34L99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 46 , Issue 1 , June 1999 , pp. 145 - 154
Copyright
Copyright © University College London 1999

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