Existence and uniqueness of Remotely Almost Periodic solutions of differential equations and applications

2025/09/14 by Diego Jaure, Jaure, Diego, Christopher Maulén +1
Mathematics · #Differential Equations and Numerical Methods #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2509.11069

openalex publication_date 2025/09/14 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28

Abstract

We establish existence and uniqueness of remotely almost periodic (RAP) solutions for nonlinear ordinary differential systems x' = A(t)x + f(t,x) + g_ν(t,x). Assuming that the linear equation x' = A(t)x admits an exponential dichotomy and that the associated Green kernel is exponentially bi-remotely almost periodic, we derive sufficient conditions guaranteeing a unique RAP solution of the perturbed system for ν in a suitable range. As an application, we obtain RAP solutions for a nonautonomous Brusselator model.

Citations

• Dichotomies and asymptotic equivalence in alternately advanced and delayed differential systems
• Almost automorphic delayed differential equations and Lasota-Wazewska model

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