Positive Solutions for Discontinuous Systems via a Multivalued Vector Version of Krasnosel’skiĭ’s Fixed Point Theorem in Cones

Abstract

We establish the existence of positive solutions for systems of second−order differential equations with discontinuous nonlinear terms. To this aim, we give a multivalued vector version of Krasnosel’skiĭ’s fixed point theorem in cones which we apply to a regularization of the discontinuous integral operator associated to the differential system. We include several examples to illustrate our theory.

Keywords

• Krasnosel’skiĭ’s fixed point theorem
• positive solutions
• discontinuous differential equations
• differential system