Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-25T04:07:33.634Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Oscillation of a Second Order Strictly Sublinear Differential Equation

Published online by Cambridge University Press:  20 November 2018

Ravi P. Agarwal ,
Cezar Avramescu  and
Octavian G. Mustafa
Ravi P. Agarwal
Affiliation:
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA e-mail: [email protected]
Cezar Avramescu
Affiliation:
Department of Mathematics, University of Craiova, Al. I. Cuza 13, Craiova, Romania e-mail: [email protected] e-mail: [email protected]
Octavian G. Mustafa
Affiliation:
Department of Mathematics, University of Craiova, Al. I. Cuza 13, Craiova, Romania e-mail: [email protected] e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

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 establish a flexible oscillation criterion based on an averaging technique that improves upon a result due to C. G. Philos.

Keywords

34C1034C1534C29oscillation theoryaveraging method
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 53 , Issue 2 , 01 June 2010 , pp. 193 - 203
Copyright
Copyright © Canadian Mathematical Society 2010

References

[1] Agarwal, R. P., Grace, S. R., and O’Regan, D., Oscillation Theory for Difference and Functional Differential Equations. Kluwer, Dordrecht, 2000.Google Scholar
[2] Agarwal, R. P., Grace, S. R., and O’Regan, D., Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations. Kluwer, Dordrecht, 2002.Google Scholar
[3] Agarwal, R. P., Grace, S. R., and O’Regan, D., Linearization of second order sublinear oscillation theorems. Commun. Appl. Anal. 8(2004), no. 2, 219–235.Google Scholar
[4] Butler, G. J., Integral averages and the oscillation of second order ordinary differential equations. SIAM J. Math. Anal. 11(1980), no. 1, 190–200. doi:10.1137/0511017Google Scholar
[5] Fite, W. B., Concerning the zeros of the solutions of certain differential equations. Trans. Amer. Math. Soc. 19(1918), no. 4, 341–352. doi:10.2307/1988973Google Scholar
[6] Kamenev, I. V., Certain specifically nonlinear oscillation theorems. Mat. Zametki 10(1971), 129–134 (in Russian).Google Scholar
[7] Kwong, M. K. and Wong, J. S. W., On the oscillation and nonoscillation of second order sublinear equations. Proc. Amer. Math. Soc. 85(1982), no. 4, 547–551. doi:10.2307/2044063Google Scholar
[8] Kwong, M. K. and Wong, J. S. W., Linearization of second-order nonlinear oscillation theorems. Trans. Amer. Math. Soc. 279(1983), no. 2, 705–722. doi:10.2307/1999562Google Scholar
[9] Naito, M., Asymptotic behavior of solutions of second order differential equations with integrable coefficients. Trans. Amer. Math. Soc. 282(1984), no. 2, 577–588. doi:10.2307/1999253Google Scholar
[10] Naito, M., Integral averages and the asymptotic behavior of solutions of second order ordinary differential equations. J. Math. Anal. Appl. 164(1992), no. 2, 370–380. doi:10.1016/0022-247X(92)90121-SGoogle Scholar
[11] Onose, H., On Butler's conjecture for oscillation of an ordinary differential equation. Quart. J. Math. Oxford 34(1983), no. 134, 235–239. doi:10.1093/qmath/34.2.235Google Scholar
[12] Philos, C. G., Integral averaging techniques for the oscillation of second order sublinear ordinary differential equations. J. Austral. Math. Soc. Ser. A 40(1986), no. 1, 111–130. doi:10.1017/S1446788700026549Google Scholar
[13] Philos, C. G., On oscillation of second order sublinear ordinary differential equations with alternating coefficients. Math. Nachr. 146(1990), 105–116. doi:10.1002/mana.19901460703Google Scholar
[14] Philos, C. G. and Purnaras, I. K., On the oscillation of second order nonlinear differential equations. Arch. Math. (Basel) 59(1992), no. 3, 260–271.Google Scholar
[15] Wintner, A., A criterion of oscillatory stability. Quart. Appl. Math. 7(1949), 115–117.Google Scholar
[16] Wong, J. S. W., A sublinear oscillation theorem. J. Math. Anal. Appl. 139(1989), 408–412. doi:10.1016/0022-247X(89)90117-0Google Scholar
[17] Wong, J. S. W., Oscillation of sublinear second order differential equations with integrable coefficients. J Math. Anal. Appl. 162(1991), no. 2, 476–481. doi:10.1016/0022-247X(91)90162-SGoogle Scholar
[18] Wong, J. S. W., On an oscillation theorem of Waltman. Canad. Appl. Math. Q. 11(2003), no. 4, 415–432.Google Scholar