Degree theory for discontinuous operators

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FPR_FPT21.pdf (333.8 KB)
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URI: https://hdl.handle.net/10347/44824
ISSN: 10.24193/fpt-ro.2021.1.10
E-ISSN: 2066-9208

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2021

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House of the Book of Science Cluj-Napoca
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Abstract

We introduce a new definition of topological degree for a meaningful class of operators which need not be continuous. Subsequently, we derive a number of fixed point theorems for such operators. As an application, we deduce a new existence result for first–order ODEs with discontinuous nonlinearities.

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Degree theory| Leray-Schauder degree| Discontinuous differential equations

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Figueroa, R., López, R., Rodríguz-López, J. (2021). Degree theory for discontinuous operators. Fixed Point Theory, 22(1), 141-156

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Rodrigo Lopez Pouso was partially supported by Ministerio de Economıa y Competitividad, Spain, and FEDER, Project MTM2016-75140-P, and Xunta de Galicia ED341D R2016/022 and GRC2015/004. Jorge Rodriguez-Lopez was financially supported by Xunta de Galicia under grant ED481A-2017/178.

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Estatística, Análise Matemática e Optimización