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

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.