# Global existence of solutions to nonlinear Volterra integral equations

## TL;DR

This paper introduces a novel method to prove the global existence of solutions for nonlinear Volterra integral equations, providing bounds based on a previously established nonlinear inequality.

## Contribution

It presents a new approach for establishing global solutions to nonlinear Volterra integral equations using a bound derived from a nonlinear inequality.

## Key findings

- Established conditions for global existence of solutions.
- Derived bounds on solutions using nonlinear inequalities.
- Validated the method for a class of nonlinear Volterra equations.

## Abstract

A new method is given for proving the global existence of the solution to nonlinear Volterra integral equations. A bound on the solution is derived. The results are based on a nonlinear inequality proved by the author earlier.