On global continuability of solutions of infinite-dimensional ordinary differential equations

Abstract

We prove necessary and sufficient conditions for global in time existence of solutions of ordinary differential equations on infinite dimensional Banach spaces and manifolds under some natural additional hypotheses, in particular, for equations with right-hand sides, given on everywhere dense subsets of phase spaces.

Keywords:

• Banach spaces
• Infinite-dimensional manifolds
• Ordinary differential equations
• Global existence of solutions

Mathematics Subject Classifications 2000::

• 34A12
• 46T05
• 58C99

Acknowledgement

The research is supported in part by RFBR Grant No. 07-01-00137.