A study of the fundamental nature of solving a system of n ordinary (nondifferential) equations is undertaken in § 1. It is found that the properties of the inverse function play an unexpectedly decisive rôle. In § 2, the results of § 1 are applied to methods of approximating eigenvalues, conjugate, focal, and σ-points previously introduced by the author. Finally, the connection between these methods and Wiman's integral is indicated.
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W. Leighton,Upper and lower bounds for eigenvalues, Journal of Mathematical Analysis and Applications,35 (1971), pp. 381–388.
W. Leighton,Computing bounds for focal points and for σ-points for second-order linear differential equations, Ordinary Differential Equations, Academic Press, New York (1972).
A. Wiman,Über die reellen Lösungen der linearen Differentialgleichungen zweiter Ordnung, Arkif für Matematik, Astronomi och Fysik,12 (1917), pp. 1–22.
Entrata in Redazione il 20 gennaio 1975.
This will acknowledge the partial support of the author by the U. S. Army Research Office (Durham) under Grant numbered DA-ARO-D-31-124-72-G27.
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Leighton, W. On approximating conjugate, focal, and σ-points for linear differential equations of second order. Annali di Matematica 107, 373–381 (1975). https://doi.org/10.1007/BF02416482
- Differential Equation
- Inverse Function
- Linear Differential Equation
- Fundamental Nature