Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-05T01:08:51.070Z Has data issue: false hasContentIssue false
  • English
  • Français

Oscillation criteria for second order differential equations with damping

Part of: Qualitative theory

Published online by Cambridge University Press:  09 April 2009

S. R. Grace
S. R. Grace
Affiliation:
Department of Mathematical SciencesKing Faud University of Petroleum and MineralsP. O. Box 1682Dhahran 31261Saudi Arabia
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.

New oscillation criteria are given for second order nonlinear ordinary differential equations with alternating coefficients. The results involve a condition obtained by Kamenev for linear differential equations. The obtained criterion for superlinear differential equations is a complement of the work established by Kwong and Wong, and Philos, for sublinear differential equations and by Yan for linear differential equations.

MSC classification

Secondary: 34C10: Oscillation theory, zeros, disconjugacy and comparison theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 49 , Issue 1 , August 1990 , pp. 43 - 54
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Bulter, G. J., ‘Integral averages and the oscillation of second order ordinary differential equations’, SIAM J. Math. Anal. 11 (1980), 190–200.Google Scholar
[2]Grace, S. R., ‘Oscillation theorems for second order nonlinear differential equations with damping’, Math. Nachr. 141 (1989), 117–127.CrossRefGoogle Scholar
[3]Grace, S. R. and Lalli, B. S., ‘An oscillation criterion for second order sublinear ordinary differential equations with damping term’, Bull. Polon. Acad. Sci. Math. 35 (1987), 181–184.Google Scholar
[4]Grace, S. R. and Lalli, B. S., ‘Oscillatory behavior of solutions of second order differential equations with alternating coefficients’, Math. Nachr. 127 (1986), 165–175.CrossRefGoogle Scholar
[5]Kamenev, I. V., ‘Integral criterion for oscillations of linear differential equations of second order’, Mat. Zametki 23 (1978), 249–251, (in Russian).Google Scholar
[6]Kwong, M. K. and Wong, J. S. W., ‘On the oscillation and nonoscillation of second order sublinear equations’, Proc. Amer. Math. Soc. 85 (1982), 547–551.CrossRefGoogle Scholar
[7]Philos, Ch. G., ‘Integral averages and second order superlinear oscillation’, Math. Nachr. 120 (1985), 127–128.CrossRefGoogle Scholar
[8]Philos, Ch. G., ‘Integral averaging techniques for the oscillation of second order sublinear ordinary differential equations’, J. Austral. Math. Soc. Ser. A 40 (1986), 111–130.CrossRefGoogle Scholar
[9]Wong, J. S. W., ‘A second order nonlinear oscillation theorem’, Proc. Amer. Math. Soc. 40 (1973), 487–491.CrossRefGoogle Scholar
[10]Wong, J. S. W., ‘An oscillation criterion for second order nonlinear differential equations’, Proc. Amer. Math. Soc. 98 (1986), 109–112.CrossRefGoogle Scholar
[11]Yan, J., ‘Oscillation theorems for second order linear differential equations with damping’, Proc. Amer. Math. Soc. 98 (1986), 276–282.CrossRefGoogle Scholar
[12]Yeh, C. C., ‘Oscillation theorems for nonlinear second order differential equations with damping terms’, Proc Amer. Math. Soc. 84 (1982), 397–402.CrossRefGoogle Scholar