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Erschienen in:
Calculus on Time Scales Kapitel lesen Erstes Kapitel lesen

2019 | OriginalPaper | Buchkapitel

14. Impulsive Functional Dynamic Equations

verfasst von : Svetlin G. Georgiev

Erschienen in: Functional Dynamic Equations on Time Scales

Verlag: Springer International Publishing

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Abstract

Let \(\mathbb {T}\) be a time scale with forward jump operator and delta differentiation operator σ and Δ, respectively.

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Vorheriges Kapitel Shift Operators
Nächstes Kapitel Linear Impulsive Dynamic Systems
Fußnoten
1
Theorem 14.3 (Krasnosel’skii Fixed Point Theorem)
Let M be a closed convex nonempty subset of a Banach space \((\mathcal B, \Vert \cdot \Vert )\) . Suppose that
1.
\(A:M\to \mathcal {B}\) is completely continuous,
 
2.
\(B: M\to \mathcal {B}\) is a contraction,
 
3.
x, y ∈ M implies Ax + By ∈ M.
 
Then the map A + B has a fixed point in M.
 
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Metadaten
Titel
Impulsive Functional Dynamic Equations
verfasst von
Svetlin G. Georgiev
Copyright-Jahr
2019
Buch
Functional Dynamic Equations on Time Scales

Print ISBN: 978-3-030-15419-6

Electronic ISBN: 978-3-030-15420-2

Copyright-Jahr: 2019

DOI
https://doi.org/10.1007/978-3-030-15420-2_14