Skip to main content
  • Book
  • © 2021

Lyapunov Inequalities and Applications

Authors:

(view affiliations)
  • Provides a comprehensive, neatly organized survey on Lyapunov-type inequalities

  • Covers applications of Lyapunov-type inequalities in boundary value problems, systems of differential equations, PDEs, dynamic equations, and more

  • Puts together content of direct relevance to advanced students in many areas of mathematical and physical sciences

Buying options

eBook
USD 139.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-69029-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book
USD 179.99
Price excludes VAT (USA)

This is a preview of subscription content, access via your institution.

Table of contents (8 chapters)

  1. Front Matter

    Pages i-xiii
  2. Lyapunov-Type Inequalities for Second-Order Linear Differential Equations

    • Ravi P. Agarwal, Martin Bohner, Abdullah Özbekler
    Pages 1-54
  3. Lyapunov-Type Inequalities for Higher-Order Linear Differential Equations

    • Ravi P. Agarwal, Martin Bohner, Abdullah Özbekler
    Pages 55-131
  4. Lyapunov-Type Inequalities for Half-Linear Differential Equations

    • Ravi P. Agarwal, Martin Bohner, Abdullah Özbekler
    Pages 133-187
  5. Lyapunov-Type Inequalities for Nonlinear Differential Systems

    • Ravi P. Agarwal, Martin Bohner, Abdullah Özbekler
    Pages 189-292
  6. Lyapunov-Type Inequalities for Fractional Differential Equations

    • Ravi P. Agarwal, Martin Bohner, Abdullah Özbekler
    Pages 293-320
  7. Lyapunov-Type Inequalities for Partial Differential Equations

    • Ravi P. Agarwal, Martin Bohner, Abdullah Özbekler
    Pages 321-380
  8. Lyapunov-Type Inequalities for Difference Equations

    • Ravi P. Agarwal, Martin Bohner, Abdullah Özbekler
    Pages 381-512
  9. Lyapunov-Type Inequalities for Dynamic Equations on Time Scales

    • Ravi P. Agarwal, Martin Bohner, Abdullah Özbekler
    Pages 513-590
  10. Back Matter

    Pages 591-607

About this book

This book provides an extensive survey on Lyapunov-type inequalities. It summarizes and puts order into a vast literature available on the subject, and sketches recent developments in this topic. In an elegant and didactic way, this work presents the concepts underlying Lyapunov-type inequalities, covering how they developed and what kind of problems they address.

This survey starts by introducing basic applications of Lyapunov’s inequalities. It then advances towards even-order, odd-order, and higher-order boundary value problems; Lyapunov and Hartman-type inequalities; systems of linear, nonlinear, and quasi-linear differential equations; recent developments in Lyapunov-type inequalities; partial differential equations; linear difference equations; and Lyapunov-type inequalities for linear, half-linear, and nonlinear dynamic equations on time scales, as well as linear Hamiltonian dynamic systems.

Senior undergraduate students and graduate students of mathematics, engineering, and science will benefit most from this book, as well as researchers in the areas of ordinary differential equations, partial differential equations, difference equations, and dynamic equations. Some background in calculus, ordinary and partial differential equations, and difference equations is recommended for full enjoyment of the content.

Keywords

  • analysis
  • Lyapunov
  • PDE
  • Lyapunov inequalities
  • boundary conditions
  • difference equations
  • differential equations
  • dynamic equations
  • Hamiltonian systems
  • time scale
  • Sturm-Liouville
  • Partial Differential Equations
  • boundary value problems
  • fractional differential equations

Authors and Affiliations

  • Department of Mathematics, Texas A&M University‑Kingsville, Kingsville, USA

    Ravi P. Agarwal

  • Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, USA

    Martin Bohner

  • Department of Mathematics, Atilim University, Ankara, Turkey

    Abdullah Özbekler

About the authors

Ravi P. Agarwal is a Professor at the Texas A&M University in Kingsville, USA, and a Distinguished University Professor of Mathematics at the Florida Institute of Technology, Melbourne, FL, USA. 

Martin Bohner is the Curators’ Distinguished Professor of Mathematics and Statistics at Missouri S&T, Rolla, Missouri, USA.

Abdullah Özbekler is a Professor at Atilim University, Department of Mathematics, Ankara, Turkey.

Bibliographic Information

  • Book Title: Lyapunov Inequalities and Applications

  • Authors: Ravi P. Agarwal, Martin Bohner, Abdullah Özbekler

  • DOI: https://doi.org/10.1007/978-3-030-69029-8

  • Publisher: Springer Cham

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

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

  • Hardcover ISBN: 978-3-030-69028-1

  • eBook ISBN: 978-3-030-69029-8

  • Edition Number: 1

  • Number of Pages: XIII, 607

  • Number of Illustrations: 2 b/w illustrations

  • Topics: Analysis, Differential Equations, Difference and Functional Equations

Buying options

eBook
USD 139.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-69029-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book
USD 179.99
Price excludes VAT (USA)