Multiple Fixed-Point Theorems and Applications in the Theory of ODEs, FDEs and PDEs covers all the basics of the subject of fixed-point theory and its applications with a strong focus on examples, proofs and practical problems, thus making it ideal as course material but also as a reference for self-study.
Many problems in science lead to nonlinear equations T x + F x = x posed in some closed convex subset of a Banach space. In particular, ordinary, fractional, partial differential equations and integral equations can be formulated like these abstract equations. It is desirable to develop fixed-point theorems for such equations. In this book, the authors investigate the 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. This book offers the reader an overview of recent developments of multiple fixed-point theorems and their applications.
About the Authors
Svetlin G. Georgiev 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 and dynamic calculus on time scales.
Khaled Zennir is assistant professor at Qassim University, KSA. He received his PhD in mathematics in 2013 from Sidi Bel Abbes University, Algeria. He obtained his Habilitation in mathematics from Constantine University, Algeria in 2015. His research interests lie in nonlinear hyperbolic partial differential equations: global existence, blow up and long-time behavior.
Reihe
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Postgraduate and Professional
Illustrationen
25 s/w Abbildungen
25 Illustrations, black and white
Maße
Höhe: 240 mm
Breite: 161 mm
Dicke: 21 mm
Gewicht
ISBN-13
978-0-367-46432-5 (9780367464325)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Khaled Zennir was born in Skikda, Algeria 1982. He received his PhD in Mathematics in 2013 from Sidi Bel Abbes 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.
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
