Fixed Point Theorems with Applications

by Karima Mebarki, Svetlin Georgiev, Smail Djebali, Khaled Zennir

Overview

As a very important part of nonlinear analysis, fixed point theory plays a key role in solvability of many complex systems from mathematics applied to chemical reactors, neutron transport, population biology, infectious diseases, economics, applied mechanics, and more.

The main aim of Fixed Point Theorems with Applications is to explain new techniques for investigation of different classes of ordinary and partial differential equations. The development of the fixed point theory parallels the advances in topology and functional analysis. Recent research has investigated not only the existence but also the positivity of solutions for various types of nonlinear equations. This book will be of interest to those working in functional analysis and its applications.

Combined with other nonlinear methods such as variational methods and the approximation methods, the fixed point theory is powerful in dealing with many nonlinear problems from the real world.

The book can be used as a textbook to develop an elective course on nonlinear functional analysis with applications in undergraduate and graduate programs in mathematics or engineering programs.

Product Details

ISBN-13:	9781032464961
Publisher:	CRC Press
Publication date:	05/12/2023
Pages:	437
Product dimensions:	6.12(w) x 9.19(h) x (d)

About the Author

Karima Mebarki is a professor in the Department of Mathematics, Bejaia University, Algeria. Her research interests are: fixed point theory, fixed point index theory, nonlinear ordinary differential equations, and boundary value problems.

Svetlin G. Georgiev is a mathematician who has worked in various aspects of mathematics. Currently, he focuses on harmonic analysis, ordinary differential equations, partial differential equations, time scale calculus, integral equations, and nonlinear analysis. He has published several books with Taylor & Francis/CRC Press.

Smail Djebali works on fixed point theory and applications in differential equations. He is currently a professor at Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia,

Khaled Zennir earned his PhD in mathematics in 2013 from Sidi Bel Abbès University, Algeria. In 2015, he received his highest diploma in Habilitation in mathematics from Constantine University, Algeria. He is currently an assistant professor at Qassim University in the Kingdom of Saudi Arabia. His research interests lie in the subjects of nonlinear hyperbolic partial differential equations: global existence, blowup, and long time behavior.

Table of Contents

1. Preliminaries. 2. Fixed Point Index for Sums of Two Operators. 3. Positive fixed points for sums of two operators. 4. Applications to ODEs. 5. Applications to Parabolic Equations. 6. Applications to Hyperbolic Equation.