Positive Solutions for a Nonlocal Resonant Problem of First Order

  • Mirosława ZimaEmail author
Conference paper
Part of the Trends in Mathematics book series (TM)


We study a first order differential system subject to a nonlocal condition. Our goal in this paper is to establish conditions sufficient for the existence of positive solutions when the considered problem is at resonance. The key tool in our approach is Leggett-Williams norm-type theorem for coincidences due to O’Regan and Zima. We conclude the paper with several examples illustrating the main result.


Positive solution Cone Resonant problem Nonlocal condition 

Mathematics Subject Classification (2010)

Primary 34B18; Secondary 34B10 



This work was completed with the partial support of the Centre for Innovation and Transfer of Natural Science and Engineering Knowledge of University of Rzeszów. The author wishes to express her thanks to the referees for careful reading of the manuscript and constructive comments.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Mathematics and Natural Sciences, Department of Functional AnalysisUniversity of RzeszówRzeszówPoland

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