Analysis of the Differential-Difference Equation $y(x+1/2)-y(x-1/2)=y^{\prime }(x)$

Abstract

In this paper we study some solution techniques of differential-difference equation $$y^{\prime }(x)=y(x+1/2)-y(x-1/2),$$ first without an initial condition and then with some initial function $h$ defined on the unit interval $[-1/2,1/2]$. We show some sufficient conditions that an initial function $h$ is admissible, i.e., it yields a unique continuous solution on some symmetric interval about $0$.

arXiv comment17 pages, 1 table, 2figures