Ordinary Differential Equations
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.
KeywordsBanach Space Cauchy Problem Poisson Bracket Proper Function Integral Curve
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- 144.Hartman, P.: Ordinary Differential Equations. John Wiley and Sons, N.Y.-L.-Sydney (1964) Google Scholar