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Asymptotic behaviour of solutions to neutral functional differential equations

Published online by Cambridge University Press:  17 April 2009

Shaozhu Chen  and
Qingguang Huang
Shaozhu Chen
Affiliation:
Department of Mathematics, Shandong University, Jinan, Shandong, 250100Peoples Republic of China
Qingguang Huang
Affiliation:
Department of Mathematics, Shandong University, Jinan, Shandong, 250100Peoples Republic of China
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Abstract

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Sufficient or necessary conditions are established so that the neutral functional differential equation [x(t) − G(t, xt)]″ + F(t, xt) = 0 has a solution which is asymptotic to a given solution of the related difference equation x(t) = G(t, xt) + a + bt, where a and b are constants.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 40 , Issue 3 , December 1989 , pp. 345 - 355
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Chen, S., ‘Asymptotic linearity of solutions of nonlinear differential equations’, Bull. Austral. Math. Soc. 35 (1987), 257–265.CrossRefGoogle Scholar
[2]Hale, J., Theory of functional differential equations (Springer-Verlag, Berlin, Heidelberg, New York, 1977).CrossRefGoogle Scholar
[3]Smart, D.R., Fixed point theorems (Cambridge Univ. Press, 1980).Google Scholar