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On the global attractivity in a generalized delay-logistic differential equation

Published online by Cambridge University Press:  24 October 2008

K. Gopalsamy
K. Gopalsamy
Affiliation:
The Flinders University of South Australia, Bedford Park, S.A. 5042, Australia
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Extract

The purpose of this article is to derive a set of ‘easily verifiable’ sufficient conditions for the local asymptotic stability of the trivial solution of

and then examine the ‘size’ of the domain of attraction of the trivial solution of the nonlinear system (1·1) with a countable number of discrete delays.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 100 , Issue 1 , July 1986 , pp. 183 - 192
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1]Bellman, R. and Cooke, K. L.. Differential-difference Equations. (Academic Press, 1963).Google Scholar
[2]Brauer, F.. Nonlinear differential equations with forcing terms. Proc. Amer. Math. Soc. 15 (1964), 758–765.CrossRefGoogle Scholar
[3]Corduneanu, C.. Functional equations with infinite delay. Boll. Un. Mat. Ital. 11, Suppl. fasc. 3 (1975) 173–181.Google Scholar
[4]Edwards, R. E.. Functional Analysis. (Reinehart and Winston, 1965).Google Scholar
[5]El'sgol'ts, L. E. and Norkin, S. B.. Introduction to the Theory and Application of Differential Equations with Deviating Arguments. (Academic Press, 1973).Google Scholar
[6]Gopalsamy, K.. Nonoscillation in a delay-logistic equation. Quart. Appl. Maths. 43 (1985), 189–197.CrossRefGoogle Scholar
[7]Hsing, D. K.. Asymptotic behaviour of the solutions of an integrodifferential system. Annali Mat. Pura. Appl. vol. CIX (1976), 235–245.CrossRefGoogle Scholar
[8]Hutchinson, G. E.. Circular causal systems in ecology. Ann. New York Acad. Sci. 50 (1948), 221–246.CrossRefGoogle ScholarPubMed
[9]Jones, G. S.. On the nonlinear differential-difference equation ƒ'(x) = -αƒ(x-1) [1+ƒ(x)]. J. Math. Anal. Appl. 4 (1962), 440–469.CrossRefGoogle Scholar
[10]Kakutani, S. and Markus, L.. On the nonlinear difference-differential equation y'(t) = [A-By(t-r)]y(t). In Contributions to the Theory of Nonlinear Oscillations (Princeton University Press, 1958).Google Scholar
[11]Stokes, A.. The application of a fixed point theorem to a variety of nonlinear stability problems. In Contributions to the Theory of Nonlinear Oscillations, vol. 5, (Princeton University Press, 1960), 173–184.Google Scholar
[12]Walther, H. O.. Stability of attractivity regions for autonomous functional differential equations. Manuscripta Math. 15 (1975), 349–369.CrossRefGoogle Scholar
[13]Wright, E. M.. A nonlinear difference-differential equation. J. Reine Angew. Math. 194 (1955), 66–87.CrossRefGoogle Scholar