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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Published inFixed point theory and algorithms for sciences and engineering Vol. 2015; no. 1; pp. 1 - 10
Main Authors Sestelo, Rubén Figueroa, Pouso, Rodrigo López
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2015
Springer Nature B.V
Subjects
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
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ISSN1687-1812
1687-1812
2730-5422
DOI10.1186/s13663-015-0472-5

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Summary: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.
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ISSN:1687-1812
1687-1812
2730-5422
DOI:10.1186/s13663-015-0472-5