# Existence theorems for a nonlinear second-order distributional differential equation

## TL;DR

This paper establishes existence theorems for nonlinear second-order distributional differential equations, encompassing measure and stochastic differential equations, using advanced integral and fixed point methods.

## Contribution

It introduces new existence results for a broad class of nonlinear second-order distributional differential equations, unifying measure and stochastic cases.

## Key findings

- Existence theorems proven for the equations
- Results are sharp, supported by illustrative examples
- Applicable to measure and stochastic differential equations

## Abstract

In this work, we are concerned with existence of solutions for a nonlinear second-order distributional differential equation, which contains measure differential equations and stochastic differential equations as special cases. The proof is based on the Leray--Schauder nonlinear alternative and Kurzweil--Henstock--Stieltjes integrals. Meanwhile, examples are worked out to demonstrate that the main results are sharp.