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Frontiers in Mathematics

Positive Solutions to Indefinite Problems

A Topological Approach

Authors: Feltrin, Guglielmo

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  • Deals with new, challenging problems in nonlinear analysis and solves several open problems and questions
  • Gives a good overview of existing methods and presents new ideas and results as well
  • Proposes open problems, research ideas and suggestions 
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eBook $29.99
$54.99 (listprice)
price for USA in USD (gross)
valid through June 30, 2020
  • ISBN 978-3-319-94238-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.99
$69.99 (listprice)
price for USA in USD
valid through June 30, 2020
  • ISBN 978-3-319-94237-7
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  • Usually dispatched within 3 to 5 business days.
About this book

This book is devoted to the study of positive solutions to indefinite problems. The monograph intelligibly provides an extensive overview of topological methods and introduces new ideas and results. Sticking to the one-dimensional setting, the author shows that compelling and substantial research can be obtained and presented in a penetrable way.
In particular, the book focuses on second order nonlinear differential equations. It analyzes the Dirichlet, Neumann and periodic boundary value problems associated with the equation and provides existence, nonexistence and multiplicity results for positive solutions. The author proposes a new approach based on topological degree theory that allows him to answer some open questions and solve a conjecture about the dependence of the number of positive solutions on the nodal behaviour of the nonlinear term of the equation. The new technique developed in the book gives, as a byproduct, infinitely many subharmonic solutions and globally defined positive solutions with chaotic behaviour. Furthermore, some future directions for research, open questions and interesting, unexplored topics of investigation are proposed.

Reviews

“The book gives a complete overview of indefinite problems, starting from the more classical results in the literature up to the very recent and novel ones. It has the advantage of being self-contained, with the prerequisites recalled in the appendices and the proofs throughout the book are provided in full detail.” (Andrea Tellini, Mathematical Reviews, November, 2019)
“This book would be suitable for graduate students and young researchers willing to learn more on this fashionable topic.” (Gennaro Infante, zbMATH 1426.34002, 2020)

Table of contents (12 chapters)

Table of contents (12 chapters)

Buy this book

eBook $29.99
$54.99 (listprice)
price for USA in USD (gross)
valid through June 30, 2020
  • ISBN 978-3-319-94238-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.99
$69.99 (listprice)
price for USA in USD
valid through June 30, 2020
  • ISBN 978-3-319-94237-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Positive Solutions to Indefinite Problems
Book Subtitle
A Topological Approach
Authors
Series Title
Frontiers in Mathematics
Copyright
2018
Publisher
Birkhäuser Basel
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-319-94238-4
DOI
10.1007/978-3-319-94238-4
Softcover ISBN
978-3-319-94237-7
Series ISSN
1660-8046
Edition Number
1
Number of Pages
XXIX, 304
Topics