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Results in Mathematics

, 74:25 | Cite as

Multiplicity Results for Operator Systems via Fixed Point Index

  • Radu Precup
  • Jorge Rodríguez-LópezEmail author
Article
  • 23 Downloads

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.

Keywords

Fixed point index positive solution operator equation Hammerstein systems \(\phi \)-Laplace equations 

Mathematics Subject Classification

34B15 34B18 47H10 47H11 

Notes

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsBabeş-Bolyai UniversityCluj-NapocaRomania
  2. 2.Departamento de Estatística, Análise Matemática e Optimización, Instituto de Matemáticas, Facultade de MatemáticasUniversidade de Santiago de CompostelaSantiagoSpain

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