Hostname: page-component-745bb68f8f-kw2vx Total loading time: 0 Render date: 2025-01-28T02:10:18.198Z Has data issue: false hasContentIssue false
  • English
  • Français

Sturmian comparison theorem for half-linear second-order differential equations

Published online by Cambridge University Press:  14 November 2011

Horng Jaan Li  and
Cheh Chih Yeh
Horng Jaan Li
Affiliation:
Chienkuo Junior College of Technology and Commerce, Chang-Hua, Taiwan, Repubic of China
Cheh Chih Yeh
Affiliation:
Department of Mathematics, National Central University, Chung-Li, Taiwan, Republic of China
Get access Rights & Permissions [Opens in a new window]

Abstract

Let φ:ℝ→ℝ be defined by φ(s) = |s|p−2s, with p > 1 a fixed number. We extend Sturm Comparison Theorem of the linear differential equation

to the nonlinear differential equation

by using the Wirtinger inequality. A Lyapunov inequality and some oscillation criteria of (E) are also given.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 6 , 1995 , pp. 1193 - 1204
Copyright
Copyright © Royal Society of Edinburgh 1995

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

1Elbert, A.. A half-linear second order differential equation. In Qualitative Theory of Differential Equations, Colloq. Math. Soc. János Bolyai 30, 153–80 (Szeged: Societas János Bolyai, 1979).Google Scholar
2Hartman, P.. Ordinary Differential Equations (New York: Wiley, 1964).Google Scholar
3Li, H. J. and Yeh, C. C.. Inequalities for a function involving its integral and derivative. Proc. Roy. Soc. Edinburgh Sect. 125A (1995), 133–51.CrossRefGoogle Scholar
4Singh, B.. Comparative study of asymptotic nonoscillation and quick oscillation of second order linear differential equations. J. Math. Phys. Sci. 4 (1974), 363–76.Google Scholar
5Swanson, C. A.. Comparison and Oscillation Theory of Linear Differential Equations (New York: Academic Press, 1968).Google Scholar
6Wong, P. K.. Sturmian Theory of Ordinary and Partial Differential Equations (Mathematics Research Centre, National Taiwan University, 1971).Google Scholar