Nonlinear Functional Analysis and Applications

✍ Scribed by Jesús Garcia-Falset; Khalid Latrach

• Publisher: De Gruyter
• Year: 2023
• Tongue: English
• Leaves: 466
• Series: De Gruyter Series in Nonlinear Analysis and Applications; 41
• Category: Library

✦ Synopsis

Nonlinear functional analysis is a central subject of mathematics with applications in many areas of geometry, analysis, fl uid and elastic mechanics, physics, chemistry, biology, control theory, optimization, game theory, economics etc. This work is devoted, in a self-contained way, to several subjects of this topic such as theory of accretive operators in Banach spaces, theory of abstract Cauchy problem, metric and topological fixed point theory. Special emphasis is given to the study how these theories can be used to obtain existence and uniqueness of solutions for several types of evolution and stationary equations. In particular, equations arising in dynamical population and neutron transport equations are discussed.

• Clear and detailed writing style
• Blends theory and applications
• Discusses the latest techniques and applications pertinent to evolution equations and boundary value problems; accretive operators and fixed-point theory

　

✦ Table of Contents

Preface
Contents
1 Fundamentals of functional analysis
2 A short introduction to semigroups of linear operators
3 Accretive operators in Banach spaces
4 Abstract Cauchy problem
5 Solvability of nonlinear evolution equations
6 Metric fixed point theorems
7 Topological fixed point theorems
8 Solvability of nonlinear boundary value problems
Bibliography
Index