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

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).