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Playing Around Resonance

An Invitation to the Search of Periodic Solutions for Second Order Ordinary Differential Equations

Birkhäuser

Authors:

  • Provides an up-to-date description of nonlinear boundary value problems
  • Theory of periodic solutions of ODEs are treated
  • Permits to fastly reach advanced scientific results and open problems in the field

Part of the book series: Birkhäuser Advanced Texts Basler Lehrbücher (BAT)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xvi
  2. Preliminaries on Hilbert Spaces

    • Alessandro Fonda
    Pages 1-29
  3. Operators in Hilbert Spaces

    • Alessandro Fonda
    Pages 31-45
  4. The Semilinear Problem

    • Alessandro Fonda
    Pages 47-70
  5. The Topological Degree

    • Alessandro Fonda
    Pages 71-99
  6. Nonresonance and Topological Degree

    • Alessandro Fonda
    Pages 101-135
  7. Playing Around Resonance

    • Alessandro Fonda
    Pages 137-156
  8. The Variational Method

    • Alessandro Fonda
    Pages 157-171
  9. At Resonance, Again

    • Alessandro Fonda
    Pages 173-191
  10. Lusternik–Schnirelmann Theory

    • Alessandro Fonda
    Pages 193-212
  11. The Poincaré–Birkhoff Theorem

    • Alessandro Fonda
    Pages 213-229
  12. A Myriad of Periodic Solutions

    • Alessandro Fonda
    Pages 231-254
  13. Back Matter

    Pages 255-309

About this book

This book provides an up-to-date description of the methods needed to face the existence of solutions to some nonlinear boundary value problems. All important and interesting aspects of the theory of periodic solutions of ordinary differential equations related to the physical and mathematical question of resonance are treated. The author has chosen as a model example the periodic problem for a second order scalar differential equation. In a paedagogical style the author takes the reader step by step from the basics to the most advanced existence results in the field.

Reviews

“Fonda’s Playing Around Resonance focuses on the material needed to develop research in ‘the existence of solutions’ to a type of nonlinear boundary value problem. In particular, he concentrates on providing the theory to research periodic solutions to second order ordinary differential equations. … it is truly geared more toward graduate students. Summing Up: Recommended. Graduate students, researchers, and faculty.” (S. L. Sullivan, Choice, Vol. 54 (11), July, 2017)

“This is an excellent book, well organized and full of well-explained results and techniques on the subject. The proofs of the theorems are rigorous and well written, the arguments are presented in a clear and pleasurable way. The final section of each chapter … provides information useful to a better understanding of the history of the results contained in the book. … used as a textbook in an advanced course dealing with periodic solutions for second-order ordinary differential equations.” (Addolorata Salvatore, Mathematical Reviews, 2017)


Authors and Affiliations

  • Dipartimento di Matematica e Geoscienze, Università degli Studi di Trieste, Trieste, Italy

    Alessandro Fonda

Bibliographic Information

  • Book Title: Playing Around Resonance

  • Book Subtitle: An Invitation to the Search of Periodic Solutions for Second Order Ordinary Differential Equations

  • Authors: Alessandro Fonda

  • Series Title: Birkhäuser Advanced Texts Basler Lehrbücher

  • DOI: https://doi.org/10.1007/978-3-319-47090-0

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG 2016

  • Hardcover ISBN: 978-3-319-47089-4Published: 22 November 2016

  • Softcover ISBN: 978-3-319-83658-4Published: 29 June 2018

  • eBook ISBN: 978-3-319-47090-0Published: 11 November 2016

  • Series ISSN: 1019-6242

  • Series E-ISSN: 2296-4894

  • Edition Number: 1

  • Number of Pages: XVI, 309

  • Number of Illustrations: 8 b/w illustrations, 1 illustrations in colour

  • Topics: Ordinary Differential Equations

Buy it now

Buying options

eBook USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 89.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access