Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-25T05:55:25.704Z Has data issue: false hasContentIssue false

Oscillation Criteria for Second Order Ordinary Differential Equations

Published online by Cambridge University Press:  13 September 2019

Manabu Naito*
Affiliation:
Department of Mathematics, Faculty of Science, Ehime University, Matsuyama 790-8577, Japan Email: [email protected]

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].

Type
Article
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), 190200. 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), 263282. https://doi.org/10.2307/2000793Google Scholar
Hartman, P., On non-oscillatory linear differential equations of second order. Amer. J. Math. 74(1952), 389400. 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), 370380. 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), 657670.Google Scholar
Philos, C. G. and Purnaras, I. K., On the oscillation of second order nonlinear differential equations. Arch. Math. (Basel) 59(1992), 260271. https://doi.org/10.1007/BF01197323Google Scholar
Wintner, A., A criterion of oscillatory stability. Quart. Appl. Math. 7(1949), 115117. 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), 633637. 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), 10941103. https://doi.org/10.4153/CJM-1993-060-3Google Scholar