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Multiplicity Results for Operator Systems via Fixed Point Index

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Abstract

We establish existence, localization and multiplicity results of positive solutions for general operator systems in ordered Banach spaces. Our main tool is the fixed point index in cones which we compute in suitable relatively open sets. In this context, each component of the fixed point operator can satisfy either the expansion condition or the compression condition. If some component of the operator is expansive, then we obtain multiplicity results. As an application, new results concerning systems of Hammerstein equations and systems of \(\phi \)-Laplace equations are deduced.

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Acknowledgements

Jorge Rodríguez-López was financially supported by Xunta de Galicia Scholarship ED481A-2017/178. The authors thank the referee for the careful reading of the manuscript and the suggested improvement.

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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, Facultade de Matemáticas, Universidade de Santiago de Compostela, 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 Jorge Rodríguez-López.

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Precup, R., Rodríguez-López, J. Multiplicity Results for Operator Systems via Fixed Point Index. Results Math 74, 25 (2019). https://doi.org/10.1007/s00025-019-0955-5

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