# Nonautonomous Young differential equations revisited

## TL;DR

This paper establishes the existence and uniqueness of solutions for nonautonomous Young differential equations under weak conditions, using advanced mathematical techniques to analyze their dependence on initial conditions.

## Contribution

It provides new proofs for solution existence and uniqueness of nonautonomous Young differential equations employing p-variation estimates and fixed point theorems.

## Key findings

- Unique solutions exist under weak conditions
- Solutions depend continuously on initial conditions
- New proof techniques for nonautonomous Young equations

## Abstract

In this paper we prove that under weak conditions a nonautonomous Young differential equation possesses a unique solution which depends continuously on initial conditions. The proofs use estimates in p-variation norms, greedy time techniques, and Gronwall-type lemma with the help of Shauder theorem of fixed points.