Sturm–Liouville eigenvalue problems

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1: 3.7 Ordinary Differential Equations

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§3.7(iv) Sturm–Liouville Eigenvalue Problems

… ►The Sturm–Liouville eigenvalue problem is the construction of a nontrivial solution of the system …

2: 18.36 Miscellaneous Polynomials

… ►The $y(x)={\widehat{L}}_n^{(k)}\left(x\right)$ satisfy a second order Sturm–Liouville eigenvalue problem of the type illustrated in Table 18.8.1, as satisfied by classical OP’s, but now with rational, rather than polynomial coefficients: …

3: 18.39 Applications in the Physical Sciences

… ►An important, and perhaps unexpected, feature of the EOP’s is now pointed out by noting that for 1D Schrödinger operators, or equivalent Sturm-Liouville ODEs, having discrete spectra with $L^2$ eigenfunctions vanishing at the end points, in this case $\pm \mathrm{\infty }$ see Simon (2005c, Theorem 3.3, p. 35), such eigenfunctions satisfy the Sturm oscillation theorem. …Both satisfy Sturm’s theorem. … ►

The Quantum Coulomb Problem

… ►In what follows the radial and spherical radial eigenfunctions corresponding to (18.39.27) are found in four different notations, with identical eigenvalues, all of which appear in the current and past mathematical and theoretical physics and chemistry literatures, regarding this central problem. … ►with eigenvalues …

4: Bibliography B

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Coefficient functions for an inhomogeneous turning-point problem. Mathematika 38 (2), pp. 217–238.

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External Links:

ISSN 0025-5793, MathReview (Archibald D. MacGillivray), ZentralBlatt

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§2.8(iii).

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Some solutions of the problem of forced convection. Philos. Mag. Series 7 20, pp. 322–343.

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External Links:

Document, ZentralBlatt

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§10.73(iv).

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Über Sturm-Liouvillesche Polynomsysteme. Math. Z. 29 (1), pp. 730–736.

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ISSN 0025-5874, Link, MathReview Entry, ZentralBlatt

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A Sturm-Liouville eigenproblem of the fourth kind: A critical latitude with equatorial trapping. Stud. Appl. Math. 101 (4), pp. 433–455.

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ISSN 0022-2526, Document, MathReview, ZentralBlatt

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§31.17(ii).

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Exponential asymptotics for an eigenvalue of a problem involving parabolic cylinder functions. Proc. Amer. Math. Soc. 114 (4), pp. 1025–1032.

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ISSN 0002-9939, FullText, MathReview, ZentralBlatt

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§12.16.

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5: Bibliography S

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Sturm oscillation and comparison theorems. In Sturm-Liouville theory, pp. 29–43.

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External Links:

Document, Link, MathReview Entry

Referenced by:

§18.36(vi), §18.39(i).

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Liouville-Green approximations via the Riccati transformation. J. Math. Anal. Appl. 116 (1), pp. 147–165.

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ISSN 0022-247X, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§2.7(iii).

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Liouville-Green-Olver approximations for complex difference equations. J. Approx. Theory 96 (2), pp. 301–322.

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ISSN 0021-9045, Document, MathReview (Dumitru Acu), ZentralBlatt

Referenced by:

§2.9(iii).

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Liouville-Green approximations for a class of linear oscillatory difference equations of the second order. J. Comput. Appl. Math. 41 (1-2), pp. 105–116.

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ISSN 0377-0427, Document, MathReview (Wan Biao Ma), ZentralBlatt

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§2.9(iii).

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A Survey on the Liouville-Green (WKB) Approximation for Linear Difference Equations of the Second Order. In Advances in Difference Equations (Veszprém, 1995), S. Elaydi, I. Győri, and G. Ladas (Eds.), pp. 567–577.

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External Links:

MathReview, ZentralBlatt

Referenced by:

§2.9(iii).

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