Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-04T19:19:11.086Z Has data issue: false hasContentIssue false
  • English
  • Français

Oscillation Criteria for Second Order Ordinary Differential Equations

Part of: Qualitative theory

Published online by Cambridge University Press:  13 September 2019

Manabu Naito
Manabu Naito*
Affiliation:
Department of Mathematics, Faculty of Science, Ehime University, Matsuyama 790-8577, Japan Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We establish new oscillation criteria for nonlinear differential equations of second order. The results here make some improvements of oscillation criteria of Butler, Erbe, and Mingarelli [2], Wong [8, 9], and Philos and Purnaras [6].

Keywords

oscillationnonoscillationEmden–Fowler

MSC classification

Primary: 34C10: Oscillation theory, zeros, disconjugacy and comparison theory
Secondary: 34C15: Nonlinear oscillations, coupled oscillators
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 2 , June 2020 , pp. 276 - 286
Copyright
© Canadian Mathematical Society 2019

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

Butler, G. J., Integral averages and the oscillation of second order ordinary differential equations. SIAM J. Math. Anal. 11(1980), 190–200. https://doi.org/10.1137/0511017Google Scholar
Butler, G. J., Erbe, L. H., and Mingarelli, A. B., Riccati techniques and variational principles in oscillation theory for linear systems. Trans. Amer. Math. Soc. 303(1987), 263–282. https://doi.org/10.2307/2000793Google Scholar
Hartman, P., On non-oscillatory linear differential equations of second order. Amer. J. Math. 74(1952), 389–400. https://doi.org/10.2307/2372004Google Scholar
Naito, M., Integral averages and the asymptotic behavior of solutions of second order ordinary differential equations. J. Math. Anal. Appl. 164(1992), 370–380. https://doi.org/10.1016/0022-247X(92)90121-SGoogle Scholar
Naito, M., Integral averaging techniques for the oscillation and nonoscillation of solutions of second order ordinary differential equations. Hiroshima Math. J. 24(1994), 657–670.Google Scholar
Philos, C. G. and Purnaras, I. K., On the oscillation of second order nonlinear differential equations. Arch. Math. (Basel) 59(1992), 260–271. https://doi.org/10.1007/BF01197323Google Scholar
Wintner, A., A criterion of oscillatory stability. Quart. Appl. Math. 7(1949), 115–117. https://doi.org/10.1090/qam/28499Google Scholar
Wong, J. S. W., An oscillation theorem for second order sublinear differential equations. Proc. Amer. Math. Soc. 110(1990), 633–637. https://doi.org/10.2307/2047903Google Scholar
Wong, J. S. W., Oscillation criteria for second order nonlinear differential equations involving integral averages. Canad. J. Math. 45(1993), 1094–1103. https://doi.org/10.4153/CJM-1993-060-3Google Scholar