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Linearization of solution operators for state-dependent delay equations: A simple example

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  • For state-dependent delay equations, it may easily happen that the equation is not differentiable. This hampers the formulation and the proof of the Principle of Linearized Stability. The fact that an equation is not differentiable does not, by itself, imply that the solution operators are not differentiable. And indeed, the aim of this paper is to present a simple example with differentiable solution operators despite of lack of differentiability of the equation. The example takes the form of a renewal equation and is motivated by a population dynamical model.
    Mathematics Subject Classification: Primary: 37N25, 92D25, 34K20; Secondary: 45D05, 58D07.


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