Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 05, pp. 1-8.

Title: A generalization of Osgood's test and a comparison criterion for
       integral equations with noise

Authors: Marcos J. Ceballos-Lira (Univ. Juarez Autonoma de Tabasco, Mexico)
         Jorge E. Macias-Diaz (Univ. Autonoma de Aguascalientes, Mexico)
	 Jose Villa  (Univ. Autonoma de Aguascalientes, Mexico)

Abstract:
 In this article, we prove a generalization of Osgood's test
 for the explosion of the solutions of initial-value problems.
 We also establish a comparison criterion for the solution of
 integral equations with noise, and provide estimations of
 the time of explosion of problems arising in the investigation
 of crack failures where the noise is the absolute value of the
 Brownian motion.

Submitted December 7, 2010. Published January 12, 2011.
Math Subject Classifications: 45G10, 45R05, 92F05, 74R10, 74R15.
Key Words: Osgood's test; comparison criterion; time of explosion;
           integral equations with noise; crack failure.