Analyticity and Nonanalyticity of Solutions of Delay-Differential Equations

John Mallet-Paret, Roger D. Nussbaum

We consider the equation $$\dot{x}(t)=f(t,x(t),x(\eta (t)))$$ with a variable time-shift $\eta (t)$. Both the nonlinearity $f$ and the shift function $\eta$ are given, and are assumed to be…