On solution manifolds for algebraic-delay systems

Abstract

Differential equations with state-dependent delays define a semiflow of continuously differentiable solution operators in general only on an associated submanifold of the Banach space $C^1([-h,0],\mathbb{R}^n)$. We extend a recent result on simplicity of these {\it solution manifolds} to systems where the delay is given by the state only implicitly in an extra equation. Such algebraic-delay systems arise from various applications. Key words: Delay differential equation, implicit state-dependent delay, solution manifold