English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We establish variants of existing results on existence, uniqueness andcontinuous dependence for a class of delay differential equations (DDE). Weapply these to continue the analysis of a differential equation from cellbiology with state-dependent delay, implicitly defined as the time when thesolution of a nonlinear ODE, that depends on the state of the DDE, reaches athreshold. For this application, previous results are restricted to initialhistories belonging to the so-called solution manifold. We here generalize theresults to a set of nonnegative Lipschitz initial histories which is muchlarger than the solution manifold and moreover convex. Additionally, we showthat the solutions define a semiflow that is continuous in the state-componentin the $C([-h,0],\R^2)$ topology, which is a variant of establisheddifferentiability of the semiflow in $C^1([-h,0],\R^2)$. For an associatedsystem we show invariance of convex and compact sets under the semiflow forfinite time.

A continuous semiflow on a space of Lipschitz functions for a differential equation with state-dependent delay from cell biology