Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 32, pp. 1-13.
Title: Existence of unstable manifolds for a certain class of delay
differential equations
Author: Hari P. Krishnan (Morgan Stanley Corporation, Chicago, USA)
Abstract:
We prove a theorem for unstable manifolds in a differential
equation with a state-dependent delay. Although the equation
cannot be formally linearized, we find an associated linear
delay equation whose dynamics are qualitatively similar near
the unstable manifold. Our proof relies upon estimates of the
derivative of a trajectory on the unstable manifold near
equilibrium.
Submitted December 1, 1999. Published April 1, 2002.
Math Subject Classifications: 34K40.
Key Words: invariant manifolds, functional differential equations.
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