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Periodic Differential Operators

Part of the Operator Theory: Advances and Applications Book Series (volume 230)

DOI: 10.1007/978-3-0348-0528-5

ISBN: 978-3-0348-0527-8

Publisher: Springer Basel - Springer Journals

Oct 4, 2012

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Chapter 1Floquet Theory

Brown, B. Malcolm; Eastham, Michael S. P.; Schmidt, Karl Michael

Pages: 1 –29

[The solutions of periodic linear systems of differential equations are not always periodic, but their global qualitative behaviour can be analysed by studying the first period interval only. After a brief summary of the necessary concepts and results from the theory of ordinary differential...
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Chapter 2Oscillations

Brown, B. Malcolm; Eastham, Michael S. P.; Schmidt, Karl Michael

Pages: 31 –65

[The Floquet theory of Chapter 1 gives an overview of the global growth properties of the solutions of periodic systems. For the purposes of spectral analysis of formally symmetric systems, the oscillations or rotations of the real-valued solutions are also of similar importance. The tool for...
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Chapter 3Asymptotics

Brown, B. Malcolm; Eastham, Michael S. P.; Schmidt, Karl Michael

Pages: 67 –111

[The main purpose of this chapter is to examine the nature of the instability intervals–first their asymptotic lengths as they recede to infinity, and second the more specialised situation when all but a finite number of them are absent. To deal with the lengths we require asymptotic estimates...
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Chapter 4Spectra

Brown, B. Malcolm; Eastham, Michael S. P.; Schmidt, Karl Michael

Pages: 113 –159

[In section 1.8 we studied the eigenvalues of the periodic, semi-periodic and twisted boundary-value problem on a period interval, and similarly those of a boundaryvalue problem with separated boundary conditions in section 2.3. We begin the present chapter with the observation that the...
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Chapter 5Perturbations

Brown, B. Malcolm; Eastham, Michael S. P.; Schmidt, Karl Michael

Pages: 161 –195

[The periodic Sturm-Liouville or Dirac operator on the whole real line has a purely absolutely continuous spectrum of band-gap structure; the regular end-point of the operator restricted to a half-line only introduces a single eigenvalue, if any, into each spectral gap. In applications, however,...

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