Multiple Fixed-Point Theorems and Applications in the Theory of ODEs, FDEs and PDEs: 1st Edition (Hardback) book cover

Multiple Fixed-Point Theorems and Applications in the Theory of ODEs, FDEs and PDEs

1st Edition

By Svetlin G. Georgiev, Khaled Zennir

Chapman and Hall/CRC

295 pages | 25 B/W Illus.

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Hardback: 9780367464325
pub: 2020-06-10
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Description

The aim of this book is to present a clear and well-organized treatment of the concept behind the development of mathematics and solution techniques. The main aim of this monograph is to study existence of multiple fixed points for some operators that are of the form T + F, where T is an expansive operator and F is a k-set contraction. The monograph offers the reader an overview of recent developments of multiple fixed point theorems and their applications.

Table of Contents

1. Fixed Point Index Theory. Multiple Fixed Point Theorems 1.1 Measures of Noncompactness 1.2 The Brower Fixed Point Theorem. The Schauder Fixed Point Theorem 1.3 Fixed Points of Strict Set Contractions 1.4 The Kronecker Index 1.5 The Brower Degree 1.5.1 Smooth Mappings 1.5.2 Homotopy Invariance 1.5.3 Continuous Mappings. Basic Properties 1.5.4 The Case f : D _ Rn !Sn1 1.6 The Leray-Schauder Degree 1.7 The Fixed Point Index for Completely Continuous Mappings 1.8 The Fixed Point Index for Strict Set Contractions 1.9 Multiple Fixed Point Theorems 2. Applications to ODEs 2.1 Periodic Solutions for First Order ODEs 2.2 BVPs for First Order ODEs 2.3 BVPs for Second Order ODEs 2.4 BVPs with Impulses 3. Applications to FDEs 3.1 Global existence for a class fractional-differential equations 3.2 Multiple Solutions for a BVP of Nonlinear Riemann-Liouville Fractional Differential Equations . 3.3 Multiple Solutions for a BVP of Nonlinear Caputo Fractional Differential Equations 4. Applications to Parabolic Equations 4.1 Differentiability of the Classical Solutions with Respect to the Initial Conditions of an IVP 4.2 Local Existence of Classical Solutions for an IBVP 4.3 Periodic Solutions 4.4 Multiple Solutions for an IBVP with Robin Boundary Conditions 5. Applications to Hyperbolic Equations 5.1 Differentiability of the Classical Solutions with Respect to the Initial Conditions for an IVP for a Class Hyperbolic Equations 5.2 Multiple Solutions for an IBVP with Robin Boundary Conditions 5.3 Periodic Solutions 6. Applications to Elliptic Equations 6.1 Multiple Solutions for an BVP with Robin Boundary Conditions 6.2 Existence and Smoothness of Navier-Stokes Equations References

About the Authors

Khaled Zennir was born in Skikda, Algeria 1982. He received his PhD in Mathematics in 2013 from Sidi Bel Abbès University, Algeria (Assist. professor). He obtained his highest diploma in Algeria (Habilitation, Mathematics) from Constantine university, Algeria in May 2015 (Assoc. professor). He is now assistant Professor at Qassim university, KSA. His research interests lie in Nonlinear Hyperbolic Partial Differential Equations: Global Existence, Blow-Up, and Long Time Behavior. Svetlin G. Georgiev (born 05 April 1974, Rouse, Bulgaria) is a mathematician who has worked in various areas of mathematics. He currently focuses on harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, dynamic calculus on time scales. 7.

About the Series

Chapman & Hall/CRC Monographs and Research Notes in Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT007000
MATHEMATICS / Differential Equations
MAT007010
MATHEMATICS / Differential Equations / Ordinary
MAT007020
MATHEMATICS / Differential Equations / Partial