On the problem of linearization for statedependent delay differential equations
Authors:
Kenneth L. Cooke and Wenzhang Huang
Journal:
Proc. Amer. Math. Soc. 124 (1996), 14171426
MSC (1991):
Primary 34K20
MathSciNet review:
1340381
Fulltext PDF Free Access
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Abstract: The local stability of the equilibrium for a general class of statedependent delay equations of the form has been studied under natural and minimal hypotheses. In particular, it has been shown that generically the behavior of the statedependent delay (except the value of near an equilibrium has no effect on the stability, and that the local linearization method can be applied by treating the delay as a constant value at the equilibrium.
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Additional Information
Kenneth L. Cooke
Affiliation:
Department of Mathematics, Pomona College, Claremont, California 91711
Email:
kcooke@pomona.edu
Wenzhang Huang
Affiliation:
Department of Mathematics, University of Alabama in Huntsville, Huntsville, Alabama 35899
Email:
huang@math.uah.edu
DOI:
http://dx.doi.org/10.1090/S0002993996034375
PII:
S 00029939(96)034375
Received by editor(s):
December 3, 1993
Additional Notes:
The first author’s research was supported in part by NSF grant DMS 9208818
The second author’s research was supported in part by NSF grant DEB 925370 to Carlos CastilloChavez and by the U.S. Army Research Office through the Mathematical Science Institute of Cornell University
Communicated by:
Hal L. Smith
Article copyright:
© Copyright 1996
American Mathematical Society
