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Positive solutions for discontinuous problems with applications to \(\phi \)-Laplacian equations

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Abstract

We establish existence and localization of positive solutions for general discontinuous problems for which a Harnack-type inequality holds. In this way, a wide range of ordinary differential problems such as higher order boundary value problems or \(\phi \)-Laplacian equations can be treated. In particular, we study the Dirichlet–Neumann problem involving the \(\phi \)-Laplacian. Our results rely on Bohnenblust–Karlin fixed point theorem which is applied to a multivalued operator defined in a product space.

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Acknowledgements

Jorge Rodríguez-López was financially supported by Xunta de Galicia Scholarship ED481A-2017/178.

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Authors and Affiliations

  1. Department of Mathematics, Babeş-Bolyai University, 400084, Cluj-Napoca, Romania

    Radu Precup

  2. Departamento de Estatística, Análise Matemática e Optimización, Instituto de Matemáticas, Universidade de Santiago de Compostela, Facultade de Matemáticas, Campus Vida, 15782, Santiago, Spain

    Jorge Rodríguez-López

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  1. Radu Precup
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  2. Jorge Rodríguez-López
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Correspondence to Radu Precup.

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Precup, R., Rodríguez-López, J. Positive solutions for discontinuous problems with applications to \(\phi \)-Laplacian equations. J. Fixed Point Theory Appl. 20, 156 (2018). https://doi.org/10.1007/s11784-018-0636-0

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  • DOI: https://doi.org/10.1007/s11784-018-0636-0

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