Asymptotic behaviors of linear advanced systems of differential equations

TL;DR

This paper investigates the long-term behavior of solutions to linear advanced differential systems with multiple variables, providing generalized theorems on convergence and exponential convergence using fixed point theory.

Contribution

It extends previous one-dimensional results to multi-dimensional systems and establishes new sufficient conditions for solution convergence.

Findings

Conditions for convergence of solutions are established.

Exponential convergence criteria are derived.

Results generalize previous one-dimensional theorems.

Abstract

In this paper, we use a Banach fixed point theorem to obtain suficient conditions satisfying the convergence and exponential convergence of solutions for the linear system of advanced differential equations. The considered system with multiple variable advanced arguments is discussed as well. The obtained theorems generalize previous results of Dung [8], from the one dimension to the n dimension.