On the solution manifolds for algebraic-delay systems

Hans-Otto Walther

doi:10.3842/umzh.v75i12.7663

Hans-Otto Walther Justus-Liebig-Universität Gießen, Mathematisches Institut der Universität, Germany

DOI: https://doi.org/10.3842/umzh.v75i12.7663

Keywords: Delay differential equation, implicit state-dependent delay, solution manifold

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.

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