# American Institute of Mathematical Sciences

August  2013, 18(6): 1663-1681. doi: 10.3934/dcdsb.2013.18.1663

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

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

Received  January 2012 Revised  March 2012 Published  March 2013

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.
Citation: Arne Ogrowsky, Björn Schmalfuss. Unstable invariant manifolds for a nonautonomous differential equation with nonautonomous unbounded delay. Discrete & Continuous Dynamical Systems - B, 2013, 18 (6) : 1663-1681. doi: 10.3934/dcdsb.2013.18.1663
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##### References:
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