Topics in Nonlinear Analysis

This book systematically introduces the theory of nonlinear analysis, providing an overview of topics such as geometry of Banach spaces, differential calculus in Banach spaces, monotone operators, and fixed point theorems. It also discusses degree theory, nonlinear matrix equations, control theory, differential and integral equations, and inclusions. The book presents surjectivity theorems, variational inequalities, stochastic game theory and mathematical biology, along with a large number of applications of these theories in various other disciplines.

Editors: Afraimovich, Valentin, Machado, José António Tenreiro, Zhang, Jiazhong (Eds.)
Presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, nonlinear dynamics in fluid and thermal dynamics, nonlinear geophysical dynamics, time-delay, and bio-network dynamics
Analyzes methods for discontinuous dynamical systems
Examines singularities in fluid and thermal dynamics and their bifurcation analysis
Illustrates analysis and control of nonlinear dynamical systems with practical applications

The main focus of this textbook, in two parts, is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. The exposition moves systematically from the basic to more sophisticated concepts with recent developments and several open problems. With challenging exercises, examples, and illustrations to help explain the rigorous analytic basis for the Navier–-Stokes equations, mean curvature flow equations, and other important equations describing real phenomena, this book is written for graduate students and researchers, not only in mathematics but also in other disciplines.

Editors: Luo, Albert C.J., Merdan, Hüseyin (Eds.)
Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes
Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology
Introduces new concepts, methods, and applications in nonlinear dynamical systems covering physical problems and mathematical modeling relevant to molecular biology, genetics, neurosciences, artificial intelligence as well as classic problems in mechanics, astronomy, and physics
Demonstrates mathematic modeling relevant to molecular biology, genetics, neurosciences, artificial intelligence as well as classic problems in mechanics, astronomy, and physics