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Stability, instability, oscillation and nonoscillation in scalar integrodifferential systems

Published online by Cambridge University Press:  17 April 2009

K. Gopalsamy
K. Gopalsamy
Affiliation:
School of Mathematics, Flinders University of South Australia, Bedford Park, South Australia 5042, Australia.
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Abstract

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Sufficient conditions are obtained for a homogeneous scalar integrodifferential system to have solutions all of which either converge to zero or oscillate or at least one of which can be nonoscillatory asymptotically.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 28 , Issue 2 , October 1983 , pp. 233 - 246
Copyright
Copyright © Australian Mathematical Society 1983

References

[1] Bellman, Richard, Cooke, Kenneth L., Differential-difference equations (Mathematics in Science and Engineering, 6. Academic Press, New York, London, 1963).CrossRefGoogle Scholar
[2] Brauer, Fred and Nohel, John A., The qualitative theory of ordinary differential equations. An introduction (Benjamin, New York, Amsterdam, 1969).Google Scholar
[3] Churchill, Ruel V., Operational mathematics, second edition (McGraw-Hill, New York, Toronto, London, 1958).Google Scholar
[4] Corduneanu, E. and Lakshmikantham, V., “Equations with unbounded delay: a survey”, Nonlin. Anal. 4 (1980), 831–877.CrossRefGoogle Scholar
[5] Goel, Narendra S., Maitra, Samaresh C. and Montroll, Elliott W., “On the Volterra and other nonlinear models of interacting populations”, Rev. Modern Phys. 43 (1971), 231–276.CrossRefGoogle Scholar
[6] Gopalsamy, K., “Stability and decay rates in a class of linear integrodifferential equations”, Funkcial Ekvacioj (to appear).Google Scholar
[7] Ladde, G.S., “Stability and oscillations in single-species processes with past memory”, Internat. J. Systems Sci. 10 (1979), 621–647.CrossRefGoogle Scholar
[8] Miller, Richard K., Nonlinear Volterra integral equations (Benjamin, Menlo Park, California, 1971).Google Scholar
[9] Smith, J. Maynard, Models in ecology (Cambridge University Press, Cambridge, 1974).Google Scholar