On the solution manifold of a differential equation with a delay which has a zero

Abstract

For a differential equation with a state-dependent delay we show that the associated solution manifold $X_f$ of codimension 1 in the space $C^1([-r,0],\mathbb{R})$ is an almost graph over a hyperplane, which implies that $X_f$ is diffeomorphic to the hyperplane. For the case considered previous results only provide a covering by 2 almost graphs.

Keywords

• delay differential equation
• state-dependent delay
• solution manifold
• almost graph