Parameter Dependence of Stable Invariant Manifolds for Delay Differential Equations under -Dichotomies

Lijun Pan

Journal of Mathematics, 2014, vol. 2014, 1-9

Abstract:

We obtain the existence of stable invariant manifolds for the nonlinear equation provided that the linear delay equation admits a nonuniform -dichotomy and is a sufficiently small Lipschitz perturbation. We show that the stable invariant manifolds are dependent on parameter . Namely, the stable invariant manifolds are Lipschitz in the parameter . In addition, we also show that nonuniform -contraction persists under sufficiently small nonlinear perturbations.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:989526

DOI: 10.1155/2014/989526

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