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arXiv · 2211.04564

Analysis of the Differential-Difference Equation $y(x+1/2)-y(x-1/2) = y'(x)$

Hailu Bikila Yadeta
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Abstract

In this paper we study some solution techniques of differential-difference equation $$ y'(x) = y(x + 1/2)- y(x- 1/2),$$ 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 $0$.

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Hailu Bikila Yadeta. 2022-11-08. Analysis of the Differential-Difference Equation $y(x+1/2)-y(x-1/2) = y'(x)$. https://arxiv.org/abs/2211.04564

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