Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-05-19T04:50:18.520Z Has data issue: false hasContentIssue false
  • English
  • Français

Comparison theorems of Sturm's type

Part of: Qualitative theory

Published online by Cambridge University Press:  26 February 2010

Jozef Džurina
Jozef Džurina
Affiliation:
Department of Mathematical Analysis, Faculty of Sciences, Šafárik University, Jesenná 5, 041 54 Košice, Slovakia
Get access

Abstract

Our aim in this paper is to establish new comparison principles. The equation

is compared with the equation

The equations considered can be in canonical or noncanonical forms.

MSC classification

Secondary: 34C10: Oscillation theory, zeros, disconjugacy and comparison theory
Type
Research Article
Information
Mathematika , Volume 41 , Issue 2 , December 1994 , pp. 312 - 321
Copyright
Copyright © University College London 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Chanturia, T. A.. Integral criteria for oscillation of solutions of higher order linear differential equations I. Differencialnye Uravnenija, 16 (1980), 470–482. (Russian)Google Scholar
2.Chanturia, T. A.. Some comparison theorems for higher order ordinary differential equations. Bull. Acad. Polon. Sci., 256 (1977), 749–756. (Russian).Google Scholar
3.Dšurina, J.Comparison theorems for nonlinear ordinary differential equations. Mat. Slovaca, 1 (1992), 299–315.Google Scholar
4.Erbe, L.. Oscillation theorems for second order linear differential equations. J. London Math. Soc. 27 (1970), 337–343.Google Scholar
5.Harris, B. J.. On the oscillation of solutions of linear differential equations. Mathematika, 31 (1984), 215–226.Google Scholar
6.Kusano, T. and Naito, M.. Oscillation criteria for general linear ordinary differential equations. Pacific J. Math., 92 (1981), 345–355.Google Scholar
7.Kusano, T. and Naito, M.. Comparison theorems for functional differential equations with deviating arguments. J. Math. Soc. Japan, 3 (1981), 509–532.Google Scholar
8.Kwong, M. K.. On certain comparison theorems for second order linear equations. Proc. Amer. Math. Soc, 84 (1982), 539–542.Google Scholar
9.Ladde, G. S., Lakshmikantham, V. and Zhang, B. G.. Oscillation Theory of Differential Equations with Deviating Arguments (Marcel Dekker, New York, 1987).Google Scholar
10.Ohriska, J.. Oscillation of differential equations and u-derivatives. Czech. Math. J., 39 (1989), 24–44.Google Scholar
11.Sturm, J. C. F.. Sur les équations différetielles du second ordre. J. Math. Pures Appl., 1 (1836), 106–186.Google Scholar