Unstable invariant manifolds for a nonautonomous differential equation with nonautonomous unbounded delay

Arne Ogrowsky; Björn Schmalfuss

doi:10.3934/dcdsb.2013.18.1663

Article Contents

2013, Volume 18, Issue 6: 1663-1681. Doi: 10.3934/dcdsb.2013.18.1663

This issue Previous Article Quadratic control problem of neutral Ornstein-Uhlenbeck processes with control delays Next Article Exponential growth rate for a singular linear stochastic delay differential equation

Unstable invariant manifolds for a nonautonomous differential equation with nonautonomous unbounded delay

Arne Ogrowsky^1, and
Björn Schmalfuss^2,

1.
Institut für Mathematik, Universität Paderborn, Warburger Straße 100, 33098 Paderborn
2.
Institut für Stochastik, Friedrich Schiller Universität Jena, Ernst Abbe Platz 2, 07737 Jena

Received: January 2012

Revised: March 2012

Published: August 2013

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Abstract

In this paper we deal with a nonautonomous differential equation with a nonautonomous delay. The aim is to establish the existence of an unstable invariant manifold to this differential equation for which we use the Lyapunov-Perron transformation. However, the delay is assumed to be unbounded which makes it necessary to use nonclassical methods.

Keywords:

Mathematics Subject Classification: Primary: 34C45, 34F05; Secondary: 37B55.

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