# Existence Results by The Method of Upper and Lower Solutions for Volterra Integral Equation on Time Scales

## TL;DR

This paper explores the use of upper and lower solution methods to establish existence and iterative solutions for Volterra integral equations on arbitrary time scales, broadening the applicability of these techniques.

## Contribution

It extends the method of upper and lower solutions and monotone iterative techniques to Volterra integral equations on arbitrary time scales, providing new existence results.

## Key findings

- Existence results for Volterra integral equations on arbitrary time scales.
- Construction of maximal and minimal solutions via monotone iterative technique.
- Application of the method to a broad class of integral equations.

## Abstract

In this article, we investigate the method of upper and lower solutions for Volterra integral equation of the first kind on arbitrary time scale $\mathbb{T}$. We establish some existence results in a certain sector. Moreover, monotone iterative technique is used to obtain maximal and minimal solutions of the considered equation.