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.
Author(s): Papageorgiou, Rǎdulescu, Repovš
Series: Springer Monographs in Mathematics
Edition: 1
Publisher: Springer
Year: 2019
Language: English
Pages: 586
Tags: Nonlinear Analysis
Front Matter ....Pages i-xi
Sobolev Spaces (Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš)....Pages 1-69
Compact Operators and Operators of Monotone Type (Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš)....Pages 71-165
Degree Theories (Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš)....Pages 167-262
Partial Order, Fixed Point Theory, Variational Principles (Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš)....Pages 263-360
Critical Point Theory (Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš)....Pages 361-456
Morse Theory and Critical Groups (Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš)....Pages 457-555
Back Matter ....Pages 557-577
