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Oscilations of higher-order neutral equations

Published online by Cambridge University Press:  17 February 2009

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

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Sufficient conditions are given for the occurrence of various types of asymptotic behaviour in the solution of a class of n th order neutral delay differential equations. The conditions are in the form of certain inequalities amongst the constants involved in the definition of the differential equations, and specify either oscillatory behavior, or asymptotic divergence, or solutions which converge to zero.

Type
Research Article
Information
The ANZIAM Journal , Volume 27 , Issue 4 , April 1986 , pp. 502 - 511
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Bellman, R. and Cooke, K. L., Differential-difference equations (Academic Press, New York, 1963).Google Scholar
[2]Brayton, R. K. and Willoughby, R. A., “On the numerical integration of a symmetric system of difference-differential equations of neutral type”, J. Math. Anal. Appl. 18 (1967), 182–189.CrossRefGoogle Scholar
[3]Driver, R. D., “Existence and continuous dependence of solutions of a neutral functional-differential equation”, Arch. Rational Mech. Anal. 19 (1965), 149–166.CrossRefGoogle Scholar
[4]Driver, R. D., “A mixed neutral system”, Nonlinear Anal.-TMA 8 (1984), 155–158.CrossRefGoogle Scholar
[5]Grammatikopoulos, M. K., Grove, E. A. and Ladas, G., “Oscillations of first order neutral delay differential equations” (to appear).Google Scholar
[6]Hale, J., Theory of functional differential equations (Springer-Verlag, New York, 1977).CrossRefGoogle Scholar
[7]Ladas, G. and Sficas, Y. G., “Oscillations of neutral delay differential equations” (to appear).Google Scholar
[8]Ladas, G. and Stavroulakis, I. P., “On delay differential inequalities of higher order”, Canad. Math. Bull. 25 (1982), 348–354.CrossRefGoogle Scholar
[9]Ladas, G. and Stavroulakis, I. P., “Oscillations of differential equations of mixed type”, J. Math. Phys. Sci. (to appear).Google Scholar
[10]Slemrod, M. and Infante, E. F., “Asymptotic stability criteria for linear systems of difference-differential equations on neutral type and their discrete analogues”, J. Math. Anal. Appl. 38 (1972), 399–415.CrossRefGoogle Scholar
[11]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, (02 1965).Google Scholar