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Abstract and Applied Analysis
Volume 2006 (2006), Article ID 39786, 17 pages
http://dx.doi.org/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).