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 ] , 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.