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Matrix representations of fourth order boundary value problems with finite spectrum. (English) Zbl 1244.34019

Summary: We show that a class of regular self-adjoint fourth order boundary value problems is equivalent to a certain class of matrix problems. Equivalent here means that they have exactly the same eigenvalues. Such an equivalence was previously known only in the second order case.

MSC:

34B09 Boundary eigenvalue problems for ordinary differential equations
34B20 Weyl theory and its generalizations for ordinary differential equations
34B24 Sturm-Liouville theory
47B25 Linear symmetric and selfadjoint operators (unbounded)
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
15A18 Eigenvalues, singular values, and eigenvectors
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References:

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