Young differential delay equations driven by H\"older continuous paths

TL;DR

This paper establishes existence, uniqueness, and regularity properties of solutions to Young differential delay equations driven by Hölder continuous paths, under weaker conditions than previously known.

Contribution

It introduces new weaker conditions for solving Young differential delay equations and analyzes the solution's dependence on initial data.

Findings

Proved existence and uniqueness of solutions.

Established continuity and differentiability with respect to initial functions.

Provided growth estimates for solutions.

Abstract

In this paper we prove the existence and uniqueness of the solution of Young differential delay equations under weaker conditions than it is known in the literature. We also prove the continuity and differentiability of the solution with respect to the initial function and give an estimate for the growth of the solution. The proofs use techniques of stopping times, Shauder-Tychonoff fixed point theorem and a Gronwall-type lemma.