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

For state-dependent delay equations, it may easily happen that the equation isnot differentiable. This hampers the formulation and the proof of the Principleof Linearized Stability. The fact that an equation is not differentiable doesnot, by itself, imply that the solution operators are not differentiable. Andindeed, the aim of this paper is to present a simple example withdifferentiable solution operators despite of lack of differentiability of theequation. The example takes the form of a renewal equation and is motivated byapopulation dynamical model.