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On the Continuous Spectra of Singular Boundary Value Problems

Published online by Cambridge University Press:  20 November 2018

C. R. Putnam
C. R. Putnam*
Affiliation:
Purdue University
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Suppose that p(t) > 0, that both p(t) and f(t) are continuous functions on the half-line 0 ≤ t < ∞, and that λ denotes a real parameter. Only real-valued functions will be considered in this paper. Let the differential equation

,

be of the limit-point type (3, p. 238), so that (1) and a linear homogeneous boundary condition

, 0 ≤ α < π,

determine a boundary value problem on 0 ≤ t < ∞ for every fixed α.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 6 , 1954 , pp. 420 - 426
Copyright
Copyright © Canadian Mathematical Society 1954

References

1. Hartman, P. and Wintner, A., A separation theorem for continuous spectra, Amer. J. of Math., 71 (1949), 650–662.Google Scholar
2. Titchmarsh, E. C., Eigenfunction expansions associated with second-order differential equations (Oxford, 1946).Google Scholar
3. Weyl, H., Ueber gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkurlicher Funktionen, Math. Ann. 68 (1910), 222–269.Google Scholar
4. Wintner, A., Stability and spectrum in the wave mechanics of lattices, Phys. Rev. 72 (1947), 81–82.Google Scholar