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The existence of periodic solutions for a class of neutral differential difference equations

Published online by Cambridge University Press:  17 February 2009

Yongshao Chen
Affiliation:
Department of Mathematics, South China Normal University, Guangzhou, 510631, China.
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Abstract

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In this paper, we study the existence of periodic solutions of the NDDE (neutral differential difference equation):

where τ > 0 and c is a real number. We obtain a sufficient condition under which (*) has at least k nonconstant oscillatory periodic solutions.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1992

References

[1] Brayton, R. K., “Nonlinear oscillations in a distributed network”, Quart. Appl. Math. 24 (1967) 289301.CrossRefGoogle 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) 182189.CrossRefGoogle Scholar
[3] Hale, J. K., Ordinary differential equations, (Wiley-Interscience, London, 1969).Google Scholar
[4] Hale, J. K., Theory of functional differential equations, (Springer Verlag, New York, 1977).CrossRefGoogle Scholar
[5] Kaplan, J. L. and Yorke, J. A., “Ordinary differential equations which yield periodic solutions of differential delay equations”, J. Math. Anal. Appl. 48 (1974) 317324.CrossRefGoogle Scholar
[6] Wen, L. Z., “The existence of periodic solutions of a class of differential difference equations”, Kexue Tongbao 32 (1987) 934935.Google Scholar