Hostname: page-component-76fb5796d-wq484 Total loading time: 0 Render date: 2024-04-28T14:37:29.983Z Has data issue: false hasContentIssue false

Oscillation theorems for second order superlinear differential equations with damping

Published online by Cambridge University Press:  09 April 2009

S. R. Grace
Affiliation:
Department of Engineering Math. Faculty of EngineeringCairo UniversityOrman, Giza 12000, Egypt
B. S. Lalli
Affiliation:
University of SaskatchewanSaskatoon S7N 0W0, Canada
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.

Some oscillation criteria for solutions of a general second order ordinary superlinear differential equation with alternating coefficients are given. The results generalize and complement some existing results in the literature.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Butler, G. J., ‘Integral averages and the oscillation of second order ordinary differential equations’, SIAM J. Math. Anal. 11 (1980), 190200.CrossRefGoogle Scholar
[2]Grace, S. R., ‘Oscillation theorems for second order nonlinear differential equations with damping’, Math. Nachr. 141 (1989), 117127.CrossRefGoogle Scholar
[3]Grace, S. R. and Lalli, B. S., ‘An oscillation criterion for second order sublinear ordinary differential equations with damping term’, Bull. Pol. Acad. Sci. Math. 35 (1987), 181184.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), 165175.CrossRefGoogle Scholar
[5]Kamaenev, I. V., ‘Integral criterion for oscillations of linear differential equations of second order’, Mat. Zametki 23 (1978), 249251. (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), 547551.CrossRefGoogle Scholar
[7]Philos, Ch. G., ‘A second order superlinear oscillation criterion’, Canad. Math. Bull. 27 (1) (1984), 102112.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), 111130.CrossRefGoogle Scholar
[9]Philos, Ch. G., ‘Oscillation criteria for second order superlinear differential equations’, Canad. J. Math. Vol. XLI No. 2 (1989), 321340.CrossRefGoogle Scholar
[10]Wong, J. S. W., ‘A second order nonlinear oscillation theorem’, Proc. Amer. Math. Soc. 40 (1973), 487491.CrossRefGoogle Scholar
[11]Wong, J. S. W., ‘An oscillation criterion for second order nonlinear differential equations’, Proc. Amer. Math. Soc. 98 (1986), 109112.CrossRefGoogle Scholar
[12]Yan, J., ‘Oscillation theorems for second order linear differential equations with damping’, Proc. Amer. Math. Soc. 98 (1986), 276282.CrossRefGoogle Scholar
[13]Yeh, C. C., ‘Oscillation theorems for nonlinear second order differential equations with damping term’, Proc. Amer. Math. Soc. 84 (1982), 397402.CrossRefGoogle Scholar