An Inverse Eigenvalue Problem of Order Four—An Infinite Case

In this paper coefficients $A(s) \in C^3 [0,1]$ and $B(s) \in C^1 [0,1]$ are constructed so that two given positive sequences $\lambda _1 < \lambda _2 < \cdots $, and $\rho _1 ,\rho _2 , \cdots $ are the eigenvalues and the corresponding normalization constants for the fourth order, self-adjoi...

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Bibliographic Details
Published inSIAM journal on mathematical analysis Vol. 9; no. 3; pp. 395 - 413
Main Author McLaughlin, Joyce R.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.06.1978
Subjects
Boundary conditions
Eigenvalues
Matrix
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Summary:In this paper coefficients $A(s) \in C^3 [0,1]$ and $B(s) \in C^1 [0,1]$ are constructed so that two given positive sequences $\lambda _1 < \lambda _2 < \cdots $, and $\rho _1 ,\rho _2 , \cdots $ are the eigenvalues and the corresponding normalization constants for the fourth order, self-adjoint, eigenvalue problem $y^{(4)} + (Ay^{(1)} )^{(1)} + By - \lambda y = 0$, $y(0) = y^{(1)} (0) = y(1) = y^{(1)} (1) = 0$, $y^{(2)} (0) = 1$.
ISSN:0036-1410
1095-7154
DOI:10.1137/0509026