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Oscillations of Neutral Delay Differential Equations

Published online by Cambridge University Press:  20 November 2018

G. Ladas
Affiliation:
Department of Mathematics University of Rhode Island Kingston, Rhode Island 02881
Y. G. Sficas
Affiliation:
Department of Mathematics University of Ioannina Ioannina 45332, Greece
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Abstract

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The oscillatory behavior of the solutions of the neutral delay differential equation

where p, τ, and a are positive constants and Q ∊ C([t0, ∞), ℝ+), are studied.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. Arino, O., Gyôri, I. and Jawhari, A., Oscillation Criteria in Delay Equations, J. Differential Equations (1984).Google Scholar
2. Bellman, R. and Cooke, K. L., “Differential-Difference Equations,” Academic Press, New York, 1963.Google Scholar
3. Driver, R. D., A Mixed Neutral System, Nonlinear Analysis, Theory, Methods and Applications 8 (1984), pp. 155158.Google Scholar
4. Driver, R. D., Existence and Continuous Dependence of Solutions of a Neutral Functional-Differential Equation, Arch. Rational Mech. Anal. 19 (1985), pp. 149166.Google Scholar
5. Hale, J., “Theory of Functional Differential Equations,” Springer-Verlag, New York, 1977.Google Scholar
6. Hunt, B. R. and Yorke, J. A., When All Solutions of Oscillate, J. Differential Equations 53 (1984), 139145.Google Scholar
7. Karakostas, G. and Staikos, V. A., μLike-Continuous Operators and Some Oscillation Results, University of Ioannina, TR #104, February 1984.Google Scholar
8. Koplatadze, R. G. and Canturia, T. A., On Oscillatory and Monotonie Solutions of First Order Differential Equations with Retarded Arguments, Differencial'nye Uravnenija 8 (1982) pp. 1463 —1465.Google Scholar
9. Kusano, T., On Even Order Functional Differential Equations with Advanced and Retarded Arguments, J. Differential Equations 45 (1982), pp. 7584.Google Scholar
10. Ladas, G., Sharp Conditions for Oscillations Caused by Delays, Applicable Anal. 9 (1979) pp. 93 —98.Google Scholar
11. Ladas, G. and Stavroulakis, I. P., On Delay Differential Inequalities of First Order, Funkcial. Eqvac, 25(1982), pp. 105113.Google Scholar
12. Ladas, G. and Stavroulakis, I. P., Oscillations Caused by Several Retarded and Advanced Arguments, J. Differential Equations 44 (1982), pp. 134152.Google Scholar
13. Ladas, G., Sficas, Y. G. and Stavroulakis, I. P., Necessary and Sufficient Conditions for Oscillations, Amer. Math. Monthly 90 (1983), pp. 637640.Google Scholar
14. Ladas, G., Sficas, Y. G. and Stavroulakis, I. P., Functional Differential Inequalities and Equations with Oscillating Coefficients, Proceedings of the Vth International Conference on “Trends in Theory and Practice of Nonlinear Differential Equations,” Marcel Dekker, Inc., 1984.Google Scholar
15. Sevelo, V. N. and Vareh, N. V., Asymptotic Methods in the Theory of Nonlinear Oscillations, Kiev “Naukova Dumka,” 1979 (Russian).Google Scholar
16. Snow, W., Existence, Uniqueness, and Stability for Nonlinear Differential-Difference Equations in the Neutral Case, N.Y.U. Courant Inst. Math. Sci. Rep. IMM-NYU 328, (February 1965).Google Scholar
17. Zahariev, A. I. and Bainov, D. D., Oscillating Properties of the Solutions of a Class of Neutral Type Functional Differential Equations, Bull. Austral. Math. Soc. 22 (1980), pp. 365372.Google Scholar