Abstract
In this chapter we present an introduction to the theory of stability. Since this is a very broad area which includes not only many topics but also various notions of stability, we mainly focus on Liapunov stability of equilibrium points and leave out topics such as the Poincaré–Bendixon theory, stability of periodic solutions, limit cycles, etc. Some of the proofs are omitted or carried out in special simple cases. For a more complete treatment the reader may consult sources such as the books by J. La Salle & S. Lefschetz, or by H. Amann, see Bibliography.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsAuthor information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Ahmad, S., Ambrosetti, A. (2014). Stability theory. In: A Textbook on Ordinary Differential Equations. UNITEXT(), vol 73. Springer, Cham. https://doi.org/10.1007/978-3-319-02129-4_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-02129-4_12
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02128-7
Online ISBN: 978-3-319-02129-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)