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In this work, we prove a generalization of Osgood's test for the explosion ofthe solutions of initial-value problems. We also establish a comparisoncriterion for the solution of integral equations with noise, and provideestimations of the time of explosion of problems arising in the investigationof crack failures where the noise is the absolute value of the Brownian motion

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