scholarly journals Oscillations and asymptotic convergence for a delay differential equation modeling platelet production

2019 ◽  
Vol 24 (6) ◽  
pp. 2417-2442
Author(s):  
Loïs Boullu ◽  
◽  
Mostafa Adimy ◽  
Fabien Crauste ◽  
Laurent Pujo-Menjouet ◽  
...  
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Equation Modeling ◽  
Asymptotic Convergence ◽  
Platelet Production ◽  
Differential Equation Modeling ◽  
Delay Differential

scholarly journals Smooth Stable Manifold for Delay Differential Equations with Arbitrary Growth Rate

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 105
Author(s):  
Lokesh Singh ◽  
Dhirendra Bahuguna
Keyword(s):  
Differential Equation ◽  
Growth Rate ◽  
Invariant Manifold ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Stable Manifold ◽  
Exponential Dichotomy ◽  
Delay Differential ◽  
Stable Invariant ◽  
Nonuniform Exponential Dichotomy

In this article, we construct a C1 stable invariant manifold for the delay differential equation x′=Ax(t)+Lxt+f(t,xt) assuming the ρ-nonuniform exponential dichotomy for the corresponding solution operator. We also assume that the C1 perturbation, f(t,xt), and its derivative are sufficiently small and satisfy smoothness conditions. To obtain the invariant manifold, we follow the method developed by Lyapunov and Perron. We also show the dependence of invariant manifold on the perturbation f(t,xt).

Sign in / Sign up

Export Citation Format

Share Document