Abstract and Applied Analysis
Volume 2006 (2006), Article ID 39786, 17 pages
doi:10.1155/AAA/2006/39786
Necessary and sufficient conditions for global-in-time existence of solutions of ordinary, stochastic, and parabolic differential equations
Faculty of Mathematics, Voronezh State University, Universitetskaya pl. 1, Voronezh 394006, Russia
Received 26 June 2005; Accepted 1 July 2005
Copyright © 2006 Yuri E. Gliklikh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We derive necessary and sufficient conditions for global-in-time
existence of solutions of ordinary differential, stochastic
differential, and parabolic equations. The conditions are
formulated in terms of complete Riemannian metrics on extended
phase spaces (conditions with two-sided estimates) or in terms of
derivatives of proper functions on extended phase spaces
(conditions with one-sided estimates).