Exponential dichotomy for a class of asymptotically autonomous delayed differential equations

2023/04/13 by Elorreaga, Heli, Gomez, Adrian
#Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2304.06838

Abstract

In this work we give a criterion to have an exponential dichotomy over all ℝ for delayed systems x'(t)=L(t)x_t, where L_±=lim_t→±∞L(t), and the systems x'(t)=L_±x_t are autonomous and hyperbolic. The proof is based in a suitable choice of weighted Sobolev spaces L^p(ℝ,μ) and W^1,p(ℝ,μ), where the involves differential operators become Fredholm's operators and this property are strongly exploited.

Related

• Dichotomies and asymptotic equivalence in alternately advanced and delayed differential systems
• Compact almost automorphic dynamics of non-autonomous differential equations with exponential dichotomy and applications to biological models with delay
• Splitting properties of linear differential systems with small delays
• Lyapunov-type characterisation of exponential dichotomies with applications to the heat and Klein-Gordon equations
• Asymptotic Behavior of Systems involving Delays: Preliminary Results