scholarly journals Discrete Characterizations of Exponential Dichotomy for Evolution Families

2003 ◽  
Vol 0052 ◽  
pp. 19-30
Author(s):  
Petre Preda ◽  
Alin Pogan ◽  
Ciprian Preda
Keyword(s):  
Exponential Dichotomy ◽  
Evolution Families

scholarly journals Discrete admissibility and exponential dichotomy for evolution families

2002 ◽  
Vol 9 (2) ◽  
pp. 383-397 ◽  
Author(s):  
Bogdan Sasu ◽  
Adina Sasu ◽  
Mihail Megan
Keyword(s):  
Exponential Dichotomy ◽  
Evolution Families

Discrete Schäffer spaces and exponential dichotomy for evolution families

2016 ◽  
Vol 185 (3) ◽  
pp. 507-523 ◽  
Author(s):  
Ciprian Preda ◽  
Oana Romina Onofrei
Keyword(s):  
Exponential Dichotomy ◽  
Evolution Families

scholarly journals Exponential dichotomy for evolution families on the real line

2006 ◽  
Vol 2006 ◽  
pp. 1-16 ◽  
Author(s):  
Adina Luminiţa Sasu
Keyword(s):  
Real Line ◽  
Exponential Dichotomy ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Evolution Family ◽  
The Real ◽  
Evolution Families ◽  
Necessary And Sufficient

We give necessary and sufficient conditions for uniform exponential dichotomy of evolution families in terms of the admissibility of the pair(Lp(ℝ,X),Lq(ℝ,X)). We show that the admissibility of the pair(Lp(ℝ,X),Lq(ℝ,X))is equivalent to the uniform exponential dichotomy of an evolution family if and only ifp≥q. As applications we obtain characterizations for uniform exponential dichotomy of semigroups.

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