# Existence of solutions of integral equations with asymptotic conditions

## TL;DR

This paper investigates the existence of solutions to integral equations on the entire real line with specific asymptotic behaviors, using a novel Banach space and fixed point index theory.

## Contribution

It introduces a new Banach space tailored for integral equations with asymptotic conditions and applies fixed point index theory to establish solution existence.

## Key findings

- Existence of solutions under certain asymptotic conditions
- Development of a new Banach space for this class of problems
- Application of fixed point index theory to the new space

## Abstract

In this work we will consider integral equations defined on the whole real line and look for solutions which satisfy some certain kind of asymptotic behavior. To do that, we will define a suitable Banach space which, to the best of our knowledge, has never been used before. In order to obtain fixed points of the integral operator, we will consider the fixed point index theory and apply it to this new Banach space.