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Bounded oscillations under the effect of retardations for differential equations of arbitrary order

Published online by Cambridge University Press:  14 February 2012

V. A. Staikos  and
I. P. Stavroulakis
V. A. Staikos
Affiliation:
Department of Mathematics, University of Ioannina, Greece
I. P. Stavroulakis
Affiliation:
Department of Mathematics, University of Ioannina, Greece
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Synopsis

This paper is concerned with the effect of the delays on the bounded solutions of the nth order n ≧ 1) differential equation

Sufficient conditions involving the retardations τJ(j = 1,2, …, m) which insure that every bounded solution of the considered equation is oscillatory are given. The results obtained generalise recent ones in [3 and 4].

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 77 , Issue 1-2 , 1977 , pp. 129 - 136
Copyright
Copyright © Royal Society of Edinburgh 1977

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References

1Ladas, G., Ladde, G. and Papadakis, J. S.Oscillations of functional-differential equations generated by delays. J. Differential Equations 12 (1972), 385–395.CrossRefGoogle Scholar
2Ladas, G., Lakshmikantham, V. and Papadakis, J. S. Oscillations of higher-order retarded differential equations generated by the retarded argument. Delay and Functional Differential Equations and their Applications (New York: Academic Press, 1972, 219–231).CrossRefGoogle Scholar
3Naito, M.Oscillations of differential inequalities with retarded arguments. Hiroshima Math. J. 5 (1975), 187–192.CrossRefGoogle Scholar
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5Shreve, W. E.Oscillation in first order nonlinear retarded argument differential equations. Proc. Amer. Math. Soc. 41 (1973), 565–568.CrossRefGoogle Scholar