In this book, the basic methods of nonlinear analysis are emphasized and illustrated in simple examples. Every considered method is motivated, explained in a general form but in the simplest possible abstract framework. Its applications are shown, particularly to boundary value problems for elementary ordinary or partial differential equations. The text is organized in two levels: a self-contained basic and, organized in appendices, an advanced level for the more experienced reader. Exercises are an organic part of the exposition and accompany the reader throughout the book.
This textbook presents a first introduction to PDEs on an elementary level, enabling the reader to understand what partial differential equations are, where they come from and how they can be solved. The intention is that the reader understands the basic principles which are valid for particular types of PDEs, and to acquire some classical methods to solve them, thus the authors restrict their considerations to fundamental types of equations and basic methods. Only basic facts from calculus and linear ordinary differential equations of first and second order are needed as a prerequisite. An elementary introduction to the basic principles of partial differential equations. With many illustrations. The book is addressed to students who intend to specialize in mathematics as well as to students of physics, engineering, and economics.
The series focuses on publishing high-level monographs that encompass the full range of current nonlinear analysis and its applications across various fields, including optimization, control theory, systems theory, mechanics, and engineering. Its primary aim is to provide the professional community with comprehensive expositions of foundational methods and results that are significant in both the theory and practical applications of nonlinear analysis. Contributions that explore the intersection of nonlinear analysis with related fields and encourage further research in these areas are especially encouraged.
The editorial team is led by Editor-in-Chief Jürgen Appell from Würzburg, Germany, with an esteemed group of Honorary and Advisory Editors including Catherine Bandle, Alain Bensoussan, Avner Friedman, Umberto Mosco, Louis Nirenberg, and Alfonso Vignoli. The Editorial Board features members from various global institutions, such as Manuel del Pino, Mikio Kato, Wojciech Kryszewski, Vicenţiu D. Rădulescu, and Simeon Reich.
Proposals for new titles are welcomed, with upcoming works planned on topics such as Morse index solutions of nonlinear elliptic equations, critical parabolic-type problems, periodic differential equations, and more, highlighting the ongoing commitment to advancing the field of nonlinear analysis.
