Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T20:32:39.885Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic behaviour, nonoscillation and stability in periodic first-order linear delay differential equations

Published online by Cambridge University Press:  14 November 2011

Ch. G. Philos
Ch. G. Philos
Affiliation:
Department of Mathematics, University of Ioannina, P.O. Box 1186, 451 10 Ioannina, Greece e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Extract

First-order scalar linear delay differential equations with periodic coefficients and constant delays are considered, where the coefficients have a common period and the delays are multiples of this period. A basic asymptotic criterion is given. Moreover, some results on the nonoscillation and on the stability of the trivial solution are obtained. An equation, which is in a sense the characteristic equation, plays an important role in establishing the results of the paper.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 6 , 1998 , pp. 1371 - 1387
Copyright
Copyright © Royal Society of Edinburgh 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Driver, R. D.. Some harmless delays. In Delay and Functional Differential Equations and their Applications, pp. 103–19 (New York: Academic Press, 1972).CrossRefGoogle Scholar
2Driver, R. D., Sasser, D. W. and Slater, M. L.. The equation x'(l)=ax(l)+bx(t-τ) with ‘small’ delay. Amer. Math. Monthly 80 (1973), 990–5.Google Scholar
3Driver, R. D.. Ordinary and Delay Differential Equations, Applied Mathematical Sciences 20 (New York: Springer, 1977).Google Scholar
4El'sgol'ts, L. E. and Norkin, S. B.. Introduction to the Theory and Application of Differential Equations with Deviating Arguments (New York: Academic Press, 1973).Google Scholar
5Huang, Q. and Chen, S.. Oscillation of neutral differential equations with periodic coefficients. Proc. Amer. Math. Soc. (1990), 997–1001.CrossRefGoogle Scholar
6Ladas, G., Philos, Ch. G. and Sficas, Y. G.. Oscillations in neutral equations with periodic coefficients. Proc. Amer. Math. Soc. (1991), 123–34.CrossRefGoogle Scholar
7Philos, Ch. G.. On the oscillation of differential equations with periodic coefficients. Proc. Amer. Math. Soc. (1991), 433–40.Google Scholar
8Philos, Ch. G.. Oscillations of some delay differential equations with periodic coefficients. J. Math. Anal. Appl. (1991), 452–75.CrossRefGoogle Scholar
9Zhang, S.. Asymptotic behaviour of solutions of periodic delay differential equations. Proc. Roy. Soc. Edinburgh Sect. A 98 (1984), 167–81.CrossRefGoogle Scholar