# Ordinary differential equations in algebras of generalized functions

## TL;DR

This paper establishes local existence, uniqueness, and Frobenius theorems for ODEs within the algebra of generalized functions, extending classical results to this generalized setting with parameter dependence.

## Contribution

It introduces a framework for solving ODEs in generalized function algebras, including composition based on c-boundedness, and proves key theorems like Frobenius in this context.

## Key findings

- Proved local existence and uniqueness of ODEs in generalized functions
- Extended results to include parameters and initial value dependence
- Established a Frobenius theorem for generalized functions

## Abstract

A local existence and uniqueness theorem for ODEs in the special algebra of generalized functions is established, as well as versions including parameters and dependence on initial values in the generalized sense. Finally, a Frobenius theorem is proved. In all these results, composition of generalized functions is based on the notion of c-boundedness.