On Poisson's state-dependent delay

Hans-Otto Walther

doi:10.3934/dcds.2013.33.365

Article Contents

2013, Volume 33, Issue 1: 365-379. Doi: 10.3934/dcds.2013.33.365

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On Poisson's state-dependent delay

Hans-Otto Walther^1,

1.
Mathematisches Institut, Universität Gießen, Arndtstr. 2, D 35392 Gießen

Received: July 2011

Revised: October 2011

Published: January 2013

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Abstract

In 1806 Poisson published one of the first papers on functional differential equations. Among others he studied an example with a state-dependent delay, which is motivated by a geometric problem. This example is not covered by recent results on initial value problems for differential equations with state-dependent delay. We show that the example generates a semiflow of differentiable solution operators, on a manifold of differentiable functions and away from a singular set. Initial data in the singular set produce multiple solutions.

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Mathematics Subject Classification: Primary: 34K05; Secondary: 37L99.

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References

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