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Higher order inverse eigenvalue problems

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Ordinary and Partial Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 964))

Abstract

The problem to be discussed is as follows. Suppose a mathematical model for a given physical problem results in a self-adjoint eigenvalue problem of the form

$$\begin{gathered}w(4) + (Aw(1))(1) + Bw - \lambda w = 0 \hfill \\\sum\limits_{i = 1}^4 {\alpha _{ij} w(i - 1)(0) = 0 = } \sum\limits_{i = 1}^4 {\beta _{ij} w(i - 1)(1),j = 1,2.} \hfill \\\end{gathered}$$

Suppose A, B and possibly αij, βij, i=1,...,4, j=1,2 are unknown but eigenvalues λi, i=1,2,... are known. A constructive technique for finding the unknown coefficients is presented. Additional data which can be required known are two normalization constants for each of the eigenfunctions.

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Authors
  1. Joyce R. McLaughlin
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W.N. Everitt B.D. Sleeman

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© 1982 Springer-Verlag

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McLaughlin, J.R. (1982). Higher order inverse eigenvalue problems. In: Everitt, W., Sleeman, B. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 964. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0065021

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  • DOI: https://doi.org/10.1007/BFb0065021

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11968-5

  • Online ISBN: 978-3-540-39561-4

  • eBook Packages: Springer Book Archive

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