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Ordinary Differential Equations

  • Yuri E. Gliklikh
Part of the Theoretical and Mathematical Physics book series (TMP)

Abstract

Many criteria for the extendability to (−∞,∞) of the solutions of differential equations in vector spaces are known (see, e.g., the bibliography in (Hartman, 1964)). The main aim of this section is to modify some conditions of this sort in such a way that they become necessary and sufficient. The trick here is the transition to extended phase spaces and an analysis of the so-called proper functions or complete Riemannian metrics on manifolds.

Keywords

Banach Space Cauchy Problem Poisson Bracket Proper Function Integral Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 144.
    Hartman, P.: Ordinary Differential Equations. John Wiley and Sons, N.Y.-L.-Sydney (1964) Google Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Mathematics DepartmentVoronezh State UniversityVoronezhRussia

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