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Stability Theory of Differential Equations

Overview


Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations. It remains a classic guide, featuring material from original research papers, including the author's own studies.
The linear equation with constant and almost-constant coefficients receives in-depth attention that includes aspects of matrix theory. No ...
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Stability Theory of Differential Equations

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Overview


Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations. It remains a classic guide, featuring material from original research papers, including the author's own studies.
The linear equation with constant and almost-constant coefficients receives in-depth attention that includes aspects of matrix theory. No previous acquaintance with the theory is necessary, since author Richard Bellman derives the results in matrix theory from the beginning. In regard to the stability of nonlinear systems, results of the linear theory are used to drive the results of Poincaré and Liapounoff. Professor Bellman then surveys important results concerning the boundedness, stability, and asymptotic behavior of second-order linear differential equations. The final chapters explore significant nonlinear differential equations whose solutions may be completely described in terms of asymptotic behavior. Only real solutions of real equations are considered, and the treatment emphasizes the behavior of these solutions as the independent variable increases without limit.
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Product Details

  • ISBN-13: 9780486462738
  • Publisher: Dover Publications
  • Publication date: 6/11/2008
  • Series: Dover Books on Mathematics Series
  • Pages: 176
  • Sales rank: 1,458,821
  • Product dimensions: 5.20 (w) x 8.40 (h) x 0.40 (d)

Table of Contents


Preface
1. Properties of Linear Systems
2. Stability, Boundedness, and Asymptotic Behavior of Solutions of Linear Systems
3. The Existence and Uniqueness of Solutions of Nonlinear Systems
4. The Stability of Solutions of Nonlinear Differential Equations
5. The Asymptotic Behavior of the Solutions of Some Nonlinear Equations of the First Order
6. The Second-order Linear Differential Equation
7. The Emden-Fowler Equation
Index
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