Positive Solutions for Discontinuous Systems via a Multivalued Vector Version of Krasnosel’skiĭ’s Fixed Point Theorem in Cones
Rodrigo López Pouso,
Radu Precup,
Jorge Rodríguez-López
Affiliations
Rodrigo López Pouso
Departamento de Estatística, Análise Matemática e Optimización, Instituto de Matemáticas, Universidade de Santiago de Compostela, Facultade de Matemáticas, Campus Vida, 15782 Santiago, Spain
Radu Precup
Department of Mathematics, Babeş-Bolyai University, 400084 Cluj, Romania
Jorge Rodríguez-López
Departamento de Estatística, Análise Matemática e Optimización, Instituto de Matemáticas, Universidade de Santiago de Compostela, Facultade de Matemáticas, Campus Vida, 15782 Santiago, Spain
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.
