Compression–Expansion Fixed Point Theorems for Decomposable Maps and Applications to Discontinuous ϕ-Laplacian problems

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URI: http://hdl.handle.net/10347/26636
ISSN: 1575-5460
E-ISSN: 1662-3592
DOI: 10.1007/s12346-021-00505-6

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2021

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Springer
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Abstract

In this paper, we prove new compression–expansion type fixed point theorems in cones for the so-called decomposable maps, that is, compositions of two upper semicontinuous multivalued maps. As an application, we obtain existence and localization of positive solutions for a differential equation with ϕ-Laplacian and discontinuous nonlinearity subject to multi-point boundary conditions. As far as we are aware, the existence results are new even in the classical case of continuous nonlinearities

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Compression–expansion fixed point theorem| Discontinuous differential equation| Positive solution| ϕ-Laplacian equation| Differential inclusion

Bibliographic citation

Rodríguez–López, J. Compression–Expansion Fixed Point Theorems for Decomposable Maps and Applications to Discontinuous ϕ-Laplacian problems. Qual. Theory Dyn. Syst. 20, 66 (2021). https://doi.org/10.1007/s12346-021-00505-6

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Jorge Rodríguez-López was partially supported by Xunta de Galicia ED431C 2019/02

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© The Author(s) 2021. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/
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Estatística, Análise Matemática e Optimización