On ordinary differential inclusions with mixed boundary conditions

TL;DR

This paper proves the existence of multiple weak solutions for Sturm-Liouville type differential inclusions with mixed boundary conditions using nonsmooth critical point theory, and applies the results to equations with discontinuous nonlinearities.

Contribution

It introduces a novel approach to establish multiple solutions for differential inclusions with set-valued reactions and mixed boundary conditions.

Findings

Existence of three weak solutions for the differential inclusion.

A multiplicity result for equations with discontinuous nonlinearities.

Application of nonsmooth critical point theory to boundary value problems.

Abstract

By means of nonsmooth critical point theory, we prove existence of three weak solutions for an ordinary differential inclusion of Sturm-Liouville type involving a general set-valued reaction term depending on a parameter, and coupled with mixed boundary conditions. As an application, we give a multiplicity result for ordinary differential equations involving discontinuous nonlinearities.