Positive solutions for discontinuous systems via a multivalued vector version of Krasnosel’skiĭ’s fixed point theorem in cones
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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˘ı’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
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Bibliographic citation
López Pouso, R.; Precup, R.; Rodríguez-López, J. Positive Solutions for Discontinuous Systems via a Multivalued Vector Version of Krasnosel’skiĭ’s Fixed Point Theorem in Cones. Mathematics 2019, 7, 451
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https://doi.org/10.3390/math7050451Sponsors
R. López Pouso was partially supported by Ministerio de Economía y Competitividad, Spain,
and FEDER, Project MTM2016-75140-P, and Xunta de Galicia ED341D R2016/022 and GRC2015/004. Jorge Rodríguez-López was partially supported by Xunta de Galicia Scholarship ED481A-2017/178
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© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution(CC BY) license (http://creativecommons.org/licenses/by/4.0/)