Universitext

Semilinear Elliptic Equations for Beginners

Existence Results via the Variational Approach

Authors: Badiale, Marino, Serra, Enrico

  • Presents a wealth of applications for techniques demonstrated within the text
  • Chapters gradually increase in difficulty, making it ideal for self-study
  • For each method of proof a prototype semilinear equation illustrates how the method works
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  • ISBN 978-0-85729-227-8
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  • Immediate eBook download after purchase
Softcover $49.95
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  • ISBN 978-0-85729-226-1
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About this Textbook

Semilinear elliptic equations are of fundamental importance for the study of geometry, physics, mechanics, engineering and life sciences. The variational approach to these equations has experienced spectacular success in recent years, reaching a high level of complexity and refinement, with a multitude of applications. Additionally, some of the simplest variational methods are evolving as classical tools in the field of nonlinear differential equations.

This book is an introduction to variational methods and their applications to semilinear elliptic problems. Providing a comprehensive overview on the subject, this book will support both student and teacher engaged in a first course in nonlinear elliptic equations. The material is introduced gradually, and in some cases redundancy is added to stress the fundamental steps in theory-building. Topics include differential calculus for functionals, linear theory, and existence theorems by minimization techniques and min-max procedures.

Requiring a basic knowledge of Analysis, Functional Analysis and the most common function spaces, such as Lebesgue and Sobolev spaces, this book will be of primary use to graduate students based in the field of nonlinear partial differential equations. It will also serve as valuable reading for final year undergraduates seeking to learn about basic working tools from variational methods and the management of certain types of nonlinear problems.

Reviews

From the reviews:

“An excellent text suitable for a graduate student or a very well-prepared undergraduate. It can easily support either a regular class or an independent study format. … The authors have done a good job of avoiding esoteric technicalities, so … that a good student could learn the notions above while studying this text. The first chapter outlines much of this material and provides references for those who need further study. … the text is on variational methods applied to semilinear elliptic boundary value problems.” (Stephen B. Robinson, Mathematical Reviews, Issue 2012 f)

“This book is a valuable reference book for specialists in the field and an excellent graduate text giving an overview of the literature on solutions of semilinear elliptic equations. … the book should be strongly recommended to anyone, either graduate student or researcher, who is interested in variational methods and their applications to partial differential equations of elliptic type .” (Vicenţiu D. Rădulescu, Zentralblatt MATH, Vol. 1214, 2011)


Table of contents (4 chapters)

  • Introduction and Basic Results

    Badiale, Marino (et al.)

    Pages 1-37

  • Minimization Techniques: Compact Problems

    Badiale, Marino (et al.)

    Pages 39-96

  • Minimization Techniques: Lack of Compactness

    Badiale, Marino (et al.)

    Pages 97-143

  • Introduction to Minimax Methods

    Badiale, Marino (et al.)

    Pages 145-189

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-0-85729-227-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-0-85729-226-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Semilinear Elliptic Equations for Beginners
Book Subtitle
Existence Results via the Variational Approach
Authors
Series Title
Universitext
Copyright
2011
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London Limited
eBook ISBN
978-0-85729-227-8
DOI
10.1007/978-0-85729-227-8
Softcover ISBN
978-0-85729-226-1
Series ISSN
0172-5939
Edition Number
1
Number of Pages
X, 199
Topics