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© 2019

Nonlinear Analysis - Theory and Methods

Benefits

  • 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

Book

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš
    Pages 1-69
  3. Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš
    Pages 71-165
  4. Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš
    Pages 167-262
  5. Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš
    Pages 263-360
  6. Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš
    Pages 361-456
  7. Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš
    Pages 457-555
  8. Back Matter
    Pages 557-577

About this book

Introduction

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.

Keywords

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

Authors and affiliations

  1. 1.Department of MathematicsNational Technical UniversityAthensGreece
  2. 2.Institute of Mathematics, Physics and MechanicsLjubljanaSlovenia
  3. 3.Faculty of Education, Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

About the authors

Nikolaos S. Papageorgiou graduated from the Massachusetts Institute of Technology and received his PhD in Applied Mathematics from Harvard University. He is Professor at the National Technical University of Athens, Greece. He has written more than 800 research papers and ten books.

Vicenţiu  Rǎdulescu received his PhD and Habilitation from the University of Paris 6 under the supervision of Haim Brezis. He is Senior Researcher at the Institute of Mathematics, Physics and Mechanics in Ljubljana, Professor at the AGH University of Science and Technology in Krakow, and Professorial Fellow at the Institute of Mathematics of the Romanian Academy. He has written more than 300 research papers and ten books.

Dušan Repovš received his PhD from Florida State University. He is Professor at the University of Ljubljana and Head of the Nonlinear Analysis, Topology, and Geometry Group at the Institute of Mathematics, Physics and Mechanics in Ljubljana. He is the author of more than 400 research papers and 3 books (Kluwer, CRC Press, European Mathematical Society). He is a member of the European Academy of Arts and Sciences.


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Reviews

“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)