# Positive and increasing solutions of perturbed Hammerstein integral equations with derivative dependence

## TL;DR

This paper investigates conditions for the existence and non-existence of non-negative, increasing solutions to perturbed Hammerstein integral equations with derivative dependence, with applications to nonlinear boundary value problems.

## Contribution

It introduces new existence and non-existence results for solutions of integral equations with derivative dependence using fixed point index theory.

## Key findings

- Established criteria for solution existence
- Identified conditions for non-existence of solutions
- Applied results to boundary value problems

## Abstract

We discuss the existence and non-existence of non-negative, non-decreasing solutions of certain perturbed Hammerstein integral equations with derivative dependence. We present some applications to nonlinear, second order boundary value problems subject to fairly general functional boundary conditions. The approach relies on classical fixed point index theory.