On the solution manifolds for algebraic-delay systems

Abstract

UDC 517.9 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 C 1 ( [ - h ,0 ] , R n ) . We extend a recent result on the simplicity of these {\it 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.