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.
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References
Hartman, P.: Ordinary Differential Equations. John Wiley and Sons, N.Y.-L.-Sydney (1964)
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© 2011 Springer-Verlag London Limited
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Gliklikh, Y.E. (2011). Ordinary Differential Equations. In: Global and Stochastic Analysis with Applications to Mathematical Physics. Theoretical and Mathematical Physics. Springer, London. https://doi.org/10.1007/978-0-85729-163-9_3
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DOI: https://doi.org/10.1007/978-0-85729-163-9_3
Publisher Name: Springer, London
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