On the problem of linearization

for state-dependent delay differential equations

Authors:
Kenneth L. Cooke and Wenzhang Huang

Journal:
Proc. Amer. Math. Soc. **124** (1996), 1417-1426

MSC (1991):
Primary 34K20

MathSciNet review:
1340381

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Abstract | References | Similar Articles | Additional Information

Abstract: The local stability of the equilibrium for a general class of state-dependent 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 state-dependent 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:
https://doi.org/10.1090/S0002-9939-96-03437-5

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 Castillo-Chavez 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