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

Rodrigo López Pouso, Radu Precup and Jorge Rodríguez-López
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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

Mathematics, 2019, vol. 7, issue 5, 1-15

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’ski?’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’ski?’s fixed point theorem; positive solutions; discontinuous differential equations; differential system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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