A Schauder-type theorem for discontinuous operators with applications to second-order BVPs

TL;DR

This paper introduces a new Schauder-type fixed point theorem for discontinuous operators in non-compact domains and applies it to solve second-order boundary value problems with discontinuous nonlinearities.

Contribution

It presents a modified Schauder-type theorem extending fixed point results to discontinuous operators and demonstrates its application to complex boundary value problems.

Findings

Established a new fixed point theorem for discontinuous operators

Applied the theorem to second-order BVPs with discontinuous nonlinearities

Provided an illustrative example demonstrating the theory's effectiveness

Abstract

We prove a new fixed point theorem of Schauder-type which applies to discontinuous operators in non-compact domains. In order to do so, we present a modification of a recent Schauder-type theorem due to Pouso. We apply our result to second-order boundary value problems with discontinuous nonlinearities. We include an example to illustrate our theory.