# A version of Krasnoselskii's compression-expansion fixed point theorem in cones for discontinuous operators with applications

## TL;DR

This paper presents a new fixed point theorem for discontinuous operators in cones, extending Krasnoselskii's classical results, and applies it to establish the existence of positive solutions for certain differential equations with discontinuous nonlinearities.

## Contribution

It introduces a novel Krasnoselskii-type fixed point theorem for discontinuous operators in cones, broadening the scope of fixed point theory.

## Key findings

- Proves a new fixed point theorem for discontinuous operators in cones.
- Establishes existence of positive solutions for differential problems with discontinuous nonlinearities.
- Demonstrates applications to boundary value problems with separated conditions.

## Abstract

We introduce a new fixed point theorem of Krasnoselskii type for discontinuous operators. As an application we use it to study the existence of positive solutions of a second-order differential problem with separated boundary conditions and discontinuous nonlinearities.