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An Oscillation Criterion for nth Order Non-Linear Differential Equations with Functional Arguments

Published online by Cambridge University Press:  20 November 2018

S. R. Grace
Affiliation:
University of Saskatchewan, Saskatoon, Sask.
B. S. Lalli
Affiliation:
University of Saskatchewan, Saskatoon, Sask.
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Abstract

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An oscillation criterion for an even order equation: x(n) + q(t)ƒ(x(t)), x[g(t)]) = 0 is provided. This criterion is an extension of a result established by Yeh for the second order equation ẍ + q(t)ƒ(x(t)), x[g(t)]) = 0.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Yeh, Cheh-Chih, An oscillation criterion for second order nonlinear differential equations with functional arguments, J. Math. Anal. Appl. 76 (1980), 72-76.Google Scholar
2. Grace, S. R. and Lalli, B. S., Oscillation Theorems for certain second order perturbed nonlinear differential equations, J. Math. Anal. Appl. 77 (1980), 205-214.Google Scholar
3. Graef, J., Rankin, S. and Spikes, P., Oscillation Theorems for perturbed nonlinear differential equations, J. Math. Anal. Appl. 65 (1978), 375-390.Google Scholar
4. Grammatikopoulos, M. K., Sficas, Y. G. and Staikas, V. A., Oscillatory properties of strongly superlinear differential equations with deviating arguments, J. Math. Anal. Appl. 67 (1979), 171-187.Google Scholar
5. Hartman, P., Ordinary differential equations, Wiley, New-York, 1964.Google Scholar
6. Kartsatos, A. G., Recent results on oscillation of solutions of forced and perturbed nonlinear differential equations of even order, in Stability of Dynamical Systems: Theory and Applications, Lect. Notes in Pure and Appl. Math. Vol. 28, pp. 17-72. Marcel Dekker, N.Y. 1977.Google Scholar
7. Mahfoud, W. E., Characterization of oscillation of solutions of the delay equation x(n)-f a(t)/(x[q(t)]) = 0, J. Diff. Eqn. 28 (1978), 437-451.Google Scholar
8. Onose, H., Oscillation of nonlinear second order equations, J. Math. Anal. Appl. 39 (1972), 122-124.Google Scholar
9. Travis, C. C., Oscillation theorems for second order equations with functional arguments, Proc. Amer. Math. Soc. 31 (1972), 199-202.Google Scholar
10. Wintner, A., A criteria of oscillatory stability, Quart. Appl. Math. 7 (1949), 115-117.Google Scholar