Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-05T13:16:42.706Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Ordering of Multi-Point Boundary Value Functions

Published online by Cambridge University Press:  20 November 2018

A. C. Peterson
A. C. Peterson*
Affiliation:
University of Nebraska, Lincoln, Nebraska
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We are concerned with the nth-order linear differential equation

1

where the coefficients are continuous. Aliev [1, 2] showed, in papers unavailable to the author that for n = 4

(see Definition 2). Theorems 1 and 5 give respectively nth-order generalizations of these two results.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 4 , December 1970 , pp. 507 - 513
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Aliev, R. G., Laws on the distributions of zeros of solutions of linear equations of fourth order, (Russian) Sb. Asp., Kazan Inst. (1964), 15-30.Google Scholar
2. Aliev, R. G., On the question of the distribution of zeros of solutions of linear differential equations of fourth order, (Russian), Recnts. of Sci. Asp. Conf. Kazan Inst., 1962.Google Scholar
3. Peterson, A. C., A theorem of Aliev, Proc. Amer. Math. Soc. 23 (1969), 364-366.Google Scholar
4. Mathsen, R. M., λ(n)-parameter families, Canad. Math. Bull. 12 (1969), 185-191.Google Scholar
5. Azbelev, N. V. and Caljuk, Z. B., On the question of distribution of zeros of solutions of linear differential equations of the third order, (Russian), Mat. Sb. (93) 51 (1960), 475-486.Google Scholar
6. Hanan, M., Oscillation criteria for third-order linear differential equations, Pac. J. Math. 11 (1961), 919-944.Google Scholar
7. Dolan, J. M., Oscillation behavior of solutions of linear differential equations of third order, Ph.D. dissertation, The Univ. of Tennessee, 1967.Google Scholar
8. Peterson, A. C., Distribution of zeros of solutions of a fourth order differential equation, Pac. J. Math. 30, (1969), 751-764 Google Scholar
9. Bogar, G. A., Properties of two point boundary value functions, Proc. Amer. Math. Soc. 23 (1969), 335-339.Google Scholar
10. Levin, A. Ju., Distribution of the zeros of solutions of a linear differential equation, Soviet Math., 818-821.Google Scholar
11. Peterson, A. C., The distribution of zeros of extremal solutions of a fourth order differential equation for the nth conjugate point, J. of D. E. (to appear).Google Scholar
12. Sherman, T. L., Properties of solutions of Nth order linear differential equations, Pac. J. Math. 15 (1965), 1045-1060.Google Scholar
13. Hartman, P. Unrestricted n-parameter families, Rend. Circ. Mat. Palermo (2) 7 (1958), 123-142.Google Scholar
14. Opial, Z., On a theorem of O. Arama, J. of D. E. 3 (1967), 88-91.Google Scholar
15. Leighton, W. and Nehari, Z., On the oscillation of solutions of self-adjoint linear differential equations of the fourth order, Trans. Amer. Math. Soc. 89 (1958), 325-377.Google Scholar
16. Gustafson, G., Ph.D. dissertation, Arizona State Univ., 1968.Google Scholar