Electron. J. Diff. Eqns., Vol. 2002(2002), No. 32, pp. 1-13.

Existence of unstable manifolds for a certain class of delay differential equations

Hari P. Krishnan

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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Hari P. Krishnan
Vice President
Morgan Stanley Corporation
Penthouse, 77 West Wacker Street
Chicago, IL 60601, USA
e-mail: Hari.Krishnan@morganstanley.com

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