Nonlinear Analysis - Theory and Methods
Buch in deiner Nähe kaufen
Beschreibung
This book emphasizes those basic abstract methods and theories that are useful in the study of nonlinear boundary value problems. The content is developed over six chapters, providing a thorough introduction to the techniques used in the variational and topological analysis of nonlinear boundary value problems described by stationary differential operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations as well as their applications to various processes arising in the applied sciences. They show how these diverse topics are connected to other important parts of mathematics, including topology, functional analysis, mathematical physics, and potential theory. Throughout the book a nice balance is maintained between rigorous mathematics and physical applications. The primary readership includes graduate students and researchers in pure and applied nonlinear analysis.
This book emphasizes those basic abstract methods and theories that are useful in the study of nonlinear boundary value problems. The content is developed over six chapters, providing a thorough introduction to the techniques used in the variational and topological analysis of nonlinear boundary value problems described by stationary differential operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations as well as their applications to various processes arising in the applied sciences. They show how these diverse topics are connected to other important parts of mathematics, including topology, functional analysis, mathematical physics, and potential theory. Throughout the book a nice balance is maintained between rigorous mathematics and physical applications. The primary readership includes graduate students and researchers in pure and applied nonlinear analysis.
Introduces the basic methods used in the qualitative mathematical analysis of nonlinear models Reveals a number of surprising interactions between several fields of mathematics, including topology, functional analysis, mathematical physics, and potential theory Can be used as supplementary reading in any course on elliptic PDEs at the graduate level or as a seminar text
Autor*in
Nikolaos S. Papageorgiou
Themen in »Nonlinear Analysis - Theory and Methods«
35-02, 49-02, 58-02 35A15, 35A16, 35J25, 35J60, 58E05 Sobolev space topological degree variational principle Morse theory nonlinear elliptic equation boundary value problem critical point theory critical groups partial differential equations
Stimmen zu »Nonlinear Analysis - Theory and Methods«
“This book is a guide to the several important tools which are used to study nonlinear boundary value problems. … This book is a serious and well-written introduction to the subject. … all the important tools for the study of nonlinear PDE are present and explained in sufficient clarity to tackle research-level problems." (Jeff Ibbotson, MAA Reviews, July 28, 2019)
()