## Differential and Integral Equations

### A note on local center manifolds for differential equations with state-dependent delay

Eugen Stumpf

#### Abstract

In this note we consider local invariant manifolds of functional differential equations $x^{\prime}(t)=f(x_{t})$ representing differential equations with state-dependent delay. Starting with a local center-stable and a local center-unstable manifold of the functional differential equation at a stationary point, we construct, by a straightforward application of the Implicit Mapping Theorem, a local center manifold.

#### Article information

Source
Differential Integral Equations, Volume 29, Number 11/12 (2016), 1093-1106.

Dates
First available in Project Euclid: 13 October 2016

https://projecteuclid.org/euclid.die/1476369331

Mathematical Reviews number (MathSciNet)
MR3557313

Zentralblatt MATH identifier
1341.34077

Subjects
Primary: 34K19: Invariant manifolds

#### Citation

Stumpf, Eugen. A note on local center manifolds for differential equations with state-dependent delay. Differential Integral Equations 29 (2016), no. 11/12, 1093--1106. https://projecteuclid.org/euclid.die/1476369331