Existence and uniqueness of periodic solution of nth-order Equations with delay in Banach space having Fourier type

TL;DR

This paper investigates the existence and uniqueness of periodic solutions for nth-order delay differential equations in Banach spaces with Fourier type, using advanced operator theory and functional analysis tools.

Contribution

It introduces a novel approach combining M-boundedness, Fourier type, and Besov spaces to establish conditions for periodic solutions in complex Banach space settings.

Findings

Established existence and uniqueness conditions for solutions

Applied Fourier type and Besov space techniques

Extended results to nth-order delay differential equations

Abstract

The aim of this work is to study the existence of a periodic solutions of nth-order differential equations with delay d dt x(t) + d 2 dt 2 x(t) + d 3 dt 3 x(t) + ... + d n dt n x(t) = Ax(t) + L(xt) + f (t). Our approach is based on the M-boundedness of linear operators, Fourier type, B s p,q-multipliers and Besov spaces.