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

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.

Keywords

• Osgood's test
• comparison criterion
• time of explosion
• integral equations with noise
• crack failure