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On approximating conjugate, focal, and σ-points for linear differential equations of second order

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Summary

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.

References

  1. [1]

    P. Hartman -A. Wintner,The asymptotic arcus variation of solutions of real linear differential equations of second order, American Journal of Mathematics,70 (1948), pp. 1–10.

  2. [2]

    W. Leighton,Upper and lower bounds for eigenvalues, Journal of Mathematical Analysis and Applications,35 (1971), pp. 381–388.

  3. [3]

    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).

  4. [4]

    A. Wiman,Über die reellen Lösungen der linearen Differentialgleichungen zweiter Ordnung, Arkif für Matematik, Astronomi och Fysik,12 (1917), pp. 1–22.

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Additional information

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

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Keywords

  • Differential Equation
  • Inverse Function
  • Linear Differential Equation
  • Fundamental Nature