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

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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)

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.

Suggested Citation

  • Rodrigo López Pouso & Radu Precup & Jorge Rodríguez-López, 2019. "Positive Solutions for Discontinuous Systems via a Multivalued Vector Version of Krasnosel’skiĭ’s Fixed Point Theorem in Cones," Mathematics, MDPI, vol. 7(5), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:451-:d:232749
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    References listed on IDEAS

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    1. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, June.
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