Asymptotic periodic solutions of differential equations with infinite delay

2023/09/06 by Nguyễn Đức Huy, Huy, Nguyen Duc, Le Anh Minh +5
Computer Science · Mathematics · #34D05 #34K14 #34K30 #34k13 #35B15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2309.02679

openalex publication_date 2023/09/06 · openalex created_date 2023/09/09 · openalex updated_date 2026/07/28

Abstract

In this paper, by using the spectral theory of functions and properties of evolution semigroups, we establish conditions on the existence, and uniqueness of asymptotic 1-periodic solutions to a class of abstract differential equations with infinite delay of the form (d u(t))/(d t)=A u(t)+L(u_t)+f(t) where A is the generator of a strongly continuous semigroup of linear operators, L is a bounded linear operator from a phase space \mathscrB to a Banach space X, u_t is an element of \mathscrB which is defined as u_t(θ)=u(t+θ) for θ≤ 0 and f is asymptotic 1-periodic in the sense that lim_{t → ∞}(f(t+1)- f(t))=0. A Lotka-Volterra model with diffusion and infinite delay is considered to illustrate our results.

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