Existence of solutions of first-order differential equations via a fixed point theorem for discontinuous operators

We use a recent Schauder-type result for discontinuous operators in order to look for solutions for first-order differential equations subject to initial functional conditions. We show how this abstract fixed-point result allows us to consider a nonlinearity which can be strongly discontinuous. Some...

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Vydáno v:	Fixed point theory and algorithms for sciences and engineering Ročník 2015; číslo 1; s. 1 - 10
Hlavní autoři:	Sestelo, Rubén Figueroa, Pouso, Rodrigo López
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Cham Springer International Publishing 01.12.2015 Springer Nature B.V
Témata:	Analysis Applications of Mathematics Differential equations Differential Geometry Existence theorems Fixed points (mathematics) Mathematical and Computational Biology Mathematics Mathematics and Statistics Nonlinearity Operators Recent Progress in Fixed Point Theory and Applications Theorems Topology Continuous Solution Extremal Solution Fixed Point Theorem Bounded Variation Point Theorem
ISSN:	1687-1812, 1687-1812, 2730-5422
On-line přístup:	Získat plný text
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Popis
Shrnutí:	We use a recent Schauder-type result for discontinuous operators in order to look for solutions for first-order differential equations subject to initial functional conditions. We show how this abstract fixed-point result allows us to consider a nonlinearity which can be strongly discontinuous. Some examples of applications and comparison with recent literature are included.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23
ISSN:	1687-1812 1687-1812 2730-5422
DOI:	10.1186/s13663-015-0472-5