On the Solution Manifolds for Algebraic-Delay Systems

Abstract

Differential equations with state-dependent delays specify a semiflow of continuously differentiable solution operators, in general, only on an associated submanifold of the Banach space C¹([−h, 0],ℝⁿ). We extend a recent result on the simplicity of these solution manifolds to systems in which the delay is given by the state only implicitly in an extra equation. These algebraic delay systems appear in various applications.