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Integral averaging techniques for the oscillation of second order sublinear ordinarry differential equations

Part of: Qualitative theory

Published online by Cambridge University Press:  09 April 2009

Ch. G. Philos
Ch. G. Philos
Affiliation:
Department of Mathematics, University of Ioannina, Ioannian, Greece
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Abstract

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New oscillation criteria are established for second order sublinear ordinary differential equations with alternating coefficients. These criteria are obtained by using an integral averaging technique and can be applied in some special cases in which other classical oscillation results are no applicable.

MSC classification

Secondary: 34C10: Oscillation theory, zeros, disconjugacy and comparison theory 34C15: Nonlinear oscillations, coupled oscillators
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 40 , Issue 1 , February 1986 , pp. 111 - 130
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Butler, G. J., “Integral averages and the oscillation of second order ordinary differential equations”, SIAM J. Math. Anal. 11 (1980), 190–200.CrossRefGoogle Scholar
[2]Hartman, P., “On nonoscillatory linear differential equations of second order”, Amer. J. Math. 74 (1952), 389–400.CrossRefGoogle Scholar
[3]Kamenev, I. V., “Some specifically nonlinear oscillation theorems”, Mat. Zametki 10 (1971), 502–505.Google Scholar
[4]Kamenev, I. V., “Oscillation criteria related to averaging of solutions of ordinary differential equations of second order”, Differencial'nye Uravneija 10 (1974), 246–252 (Differential Equations 10 (1974), 179–183).Google Scholar
[5]Kura, T., “Oscillation theorems for a second order sublinear ordinary differential equation”, Proc. Amer. Math. Soc. 84 (1982), 535–538.CrossRefGoogle Scholar
[6]Kwong, Man Kan and Wong, J. S. W., “On an oscillation theorem of Belohorec”, SIAM J. Math. Anal. 14 (1983), 474–476.CrossRefGoogle Scholar
[7]Kwong, Man Kan 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
[8]Onose, H., “Oscillation criteria for second order nonlinear differential equations”, Proc. Amer. Math. Soc. 51 (1975), 67–73.CrossRefGoogle Scholar
[9]Philos, Ch. G., “Oscillation of sublinear differential equations of second order”, Nonlinear Anal. 7 (1984), 1071–1080.CrossRefGoogle Scholar
[10]Philos, Ch. G., “A second order superlinear oscillation criterion”, Canad. Math. Bull. 27 (1984), 102–112.CrossRefGoogle Scholar
[11]Ševelo, V. N., “Problems, methods and fundamental results in the theory of oscillation of solutions of nonlinear non-autonomous ordinary differential equations”, pp. 142–157, Proceedings of the 2nd All- Union Conference on Theoretical and Applied Mechanics, Moscow, 1965.Google Scholar
[12]Wintner, A., “A criterion of oscillatory stability”, Quart. Appl. Math. 7 (1949), 115–117.CrossRefGoogle Scholar
[13]Wong, J. S. W., “On the second order nonlinear oscillation”, Funkcial. Ekvac. 11 (1968), 207–234.Google Scholar
[14]Wong, J. S. W., “A second order nonlinear oscillation theorem”, Proc. Amer. Math. Soc. 40 (1973), 487–491.CrossRefGoogle Scholar
[15]Wong, J. S. W., “Oscillation theorems for second order nonlinear differential equations”, Bull. Inst. Math. Acad. Sinica 3 (1975), 283–309.Google Scholar
[16]Wong, J. S. W., “On the generalized Emden-Fowler equation”, SIAM Rev. 17 (1975), 339–360.CrossRefGoogle Scholar