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Lower Bounds for the Essential Spectrum of Fourth-Order Differential Operators
Published online by Cambridge University Press: 20 November 2018
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In this paper, we seek to determine the greatest lower bound of the essential spectrum of self-adjoint singular differential operators of the form
1
where 0 ≦ x < ∞. In the event that this bound is + ∞, our results will yield criteria for the discreteness of the spectrum of (1).
Such bounds have been established by Friedrichs (3) for Sturm-Liouville operators of the form
and our techniques will be closely related to those of (3). However, instead of studying the solutions of
2
directly, we shall exploit the intimate connection between the infimum of the essential spectrum of (1) and the oscillation properties of (2).
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- Research Article
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- Copyright © Canadian Mathematical Society 1969
References
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