Degree theory for discontinuous operators

2017/01/09 by Figueroa, Rubén, Pouso, Rodrigo López, López, Jorge Rodríguez
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1701.02260

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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