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A historical note on Sturmian theory. (English) Zbl 0323.34031


MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
34-03 History of ordinary differential equations
34A30 Linear ordinary differential equations and systems
Full Text: DOI

References:

[1] Bôcher, M., The published and unpublished work of Charles Sturm on algebraic and differential equations, Bull. Amer. Math. Soc., 18, 1-18 (1911-1912) · JFM 42.0058.02
[2] Bôcher, M., Boundary problems in one dimension, (Proc. Fifth Int. Congress of Mathematics, I. Proc. Fifth Int. Congress of Mathematics, I, Cambridge (1912)), 163-195 · JFM 44.0440.01
[3] Hartman, P.; Wintner, A., On the assignment of asymptotic values for the solutions of linear differential equations of the second order, Amer. J. Math., 77, 475-483 (1955) · Zbl 0064.33205
[4] Hartman, P., Ordinary Differential Equations (1964), Wiley · Zbl 0125.32102
[5] Leighton, W.; Morse, M., Singular quadratic functionals, Trans. Amer. Soc., 40, 252-286 (1936) · JFM 62.0577.02
[6] Porter, M. B., On the roots of functions connected by a linear recurrent relation of the second order, Ann. Math., 3, 55-70 (1902) · JFM 33.0483.01
[7] Reid, W. T., Principal solutions of nonoscillatory self-adjoint linear differential systems, Pacific J. Math., 8, 147-169 (1958) · Zbl 0102.30005
[8] Reid, W. T., Generalized linear differential systems, J. Math. Mech., 8, 705-726 (1959) · Zbl 0094.06001
[9] Reid, W. T., Generalized linear differential systems and related Riccati matrix integral equations, Illinois J. Math., 10, 701-722 (1966) · Zbl 0199.14001
[10] Reid, W. T., Ordinary Differential Equations (1971), Wiley · Zbl 0212.10901
[11] Sturm, J. C.F., Mémoire sur les équations différentielles linéaires du second ordre, J. Math. Pures Appl., 1, 106-186 (1836)
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