Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T16:02:59.775Z Has data issue: false hasContentIssue false

Oscillation Criteria For Second Order Superlinear Differential Equations

Published online by Cambridge University Press:  20 November 2018

CH. G. Philos*
Affiliation:
University of Ioannina, Ioannina, Greece
Rights & Permissions [Opens in a new window]

Extract

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.

This paper is concerned with the question of oscillation of the solutions of second order superlinear ordinary differential equations with alternating coefficients.

Consider the second order nonlinear ordinary differential equation

where a is a continuous function on the interval [t0, ∞), t0 > 0, and / is a continuous function on the real line R, which is continuously differentia t e , except possibly at 0, and satisfies.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Butler, G.J., Oscillation theorems for a nonlinear analogue of Hill's equation, Quart. J. Math. Oxford (2) 27 (1976), 159171.Google Scholar
2. Butler, G.J., The existence of continuable solutions of a second order differential equation, Can. J. Math. 29(1977), 472479.Google Scholar
3. Butler, G.J., Integral averages and the oscillation of second order ordinary differential equations, SIAM J. Math. Anal. 11 (1980), 190200.Google Scholar
4. Butler, G.J. and Erbe, L.H., A generalization of Olech-Opial-Wazewski oscillation criteria to second order nonlinear equations, Nonlinear Anal. 11 (1987), 207219.Google Scholar
5. Kamenev, I.V., Certain specifically nonlinear oscillation theorems, Mat. Zametki 10 (1971), 129134 (Math. Notes 10 (1971), 502505).Google Scholar
6. Kamenev, I.V., Oscillation criteria related to averaging of solutions of ordinary differential equations of second order, Differensial'nye Uravneniya 10 (1974), 246252 (Differential Equations 10 (1974), 179-183).Google Scholar
7. Kamenev, I.V., An integral criterion for oscillation of linear differential equations of second order, Mat. Zametki 23 (1978), 249251 (Math. Notes 23 (1978), 136-138.Google Scholar
8. Kwong, M.K. and Wong, J.S.W., Linearization of second order nonlinear oscillation theorems, Trans. Amer. Math. Soc. 279 (1983), 705722.Google Scholar
9. Onose, H., Oscillation criteria for second order nonlinear differential equations, Proc. Amer. Math. Soc. 57 (1975), 6773.Google Scholar
10. Philos, Ch. G., A second order superlinear oscillation criterion, Canad. Math. Bull. 27 (1984), 102112.Google Scholar
11. Philos, Ch. G., Integral averages and second order superlinear oscillation, Math. Nachr. 120 (1985), 127138.Google Scholar
12. Philos, Ch. G., An oscillation criterion for superlinear differential equations of second order, J. Math. Anal. Appl. (to appear).Google Scholar
13. Wintner, A., A criterion of oscillatory stability, Quart. Appl. Math. 7 (1949), 115117.Google Scholar
14. Wong, J.S.W., On second order nonlinear oscillation, Funkcial. Ekvac. 11 (1968), 207234.Google Scholar
15. Wong, J.S.W., A second order nonlinear oscillation theorem, Proc. Amer. Math. Soc. 40 (1973), 487491.Google Scholar
16. Wong, J.S.W., Oscillation theorems for second order nonlinear differential equations, Bull. Inst. Math. Acad. Sinica 3 (1975), 283309.Google Scholar
17. Wong, J.S.W., On the generalized Emden-Fowler equation, SIAM Rev. 17 (1975), 339360.Google Scholar
18. Wong, J.S.W., An oscillation criterion for second order nonlinear differential equations, Proc. Amer. Math. Soc. 95(1986), 109112.Google Scholar