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Global attractivity in the delay logistic equation with variable parameters

Published online by Cambridge University Press:  24 October 2008

B. G. Zhang  and
K. Gopalsamy
B. G. Zhang
Affiliation:
School of Mathematical Sciences, Flinders University of South Australia, Bedford Park, S.A. 5042, Australia
K. Gopalsamy
Affiliation:
School of Mathematical Sciences, Flinders University of South Australia, Bedford Park, S.A. 5042, Australia
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Abstract

Using a non-linear variation of constants formula, sufficient conditions are derived for the global asymptotic stability of the trivial solution of

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 107 , Issue 3 , May 1990 , pp. 579 - 590
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

REFERENCES

[1]Barbalat, I.. Systemes d'equations differentielle d'oscillations nonlineaires. Rev. Roumaine Math. Pures Appl. 4 (1959), 267–270.Google Scholar
[2]Brauer, F.. Perturbations of nonlinear systems of differential equations II. J. Math. Anal. Appl. 17, 418–434 (1967).CrossRefGoogle Scholar
[3]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
[4]Halanay, A.. Differential Equations (Academic Press, 1966).Google Scholar
[5]Hastings, S. P.. Variation of parameters for nonlinear differential-difference equations. Proc. Amer. Math. Soc. 19 (1968), 1211–1216.CrossRefGoogle Scholar
[6]Jones, G. S.. On the nonlinear differential-difference equation f′(x) = –αf(x–1)[1+f(x)]. J. Math. Anal. Appl. 4 (1962), 440–469.CrossRefGoogle Scholar
[7]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
[8]Marlin, J. A. and Struble, R. A.. Asymptotic equivalence of nonlinear systems. J. Differential Equations 6 (1969), 578–596.CrossRefGoogle Scholar
[9]Shanholt, G. A.. A nonlinear variation of constants formula for functional differential equations. Math. Systems Theory 6 (1972–1973), 343–352.CrossRefGoogle Scholar
[10]Wright, E. M.. A nonlinear difference-differential equation. J. Reine Angew. Math. 194 (1955), 66–87.CrossRefGoogle Scholar
[11]Zhang, B. G. and Gopalsamy, K.. Oscillation and nonoscillation in a nonautonomous delay logistic equation. Quart. Appl. Math. 46 (1988), 267–273.CrossRefGoogle Scholar
[12]Zhang, B. G. and Gopalsamy, K.. Global attractivity and oscillations in periodic delay logistic equation. J. Math. Anal. Appl. (To appear.)Google Scholar