Multiplicity results for operator systems via fixed point index

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 φ-Laplacian equations are deduced.

Authors

Radu Precup
Babes-Bolyai University, Cluj-Napoca, Romania

Jorge Rodríguez-López
Universidade de Santiago de Compostela, Santiago, Spain

Keywords

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Paper coordinates

R. Precup, J. Rodríguez-López, Multiplicity results for operator systems via fixed point index, Results Math. 74 (2019), art. no. 25, https://doi.org/10.1007/s00025-019-0955-5

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About this paper

Journal

Results in Mathematics

Publisher Name

Springer

Print ISSN

1422-6383

Online ISSN

1420-9012

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