Regularization of non-linear measure differential equations

Abstract

The Cauchy problem for a non-linear system of regularized measure differential equations is studied. It is proved that the solutions of the regularized problems converges to a solution of an integral equation involving measures. In general this equation differs from the formal one corresponding to the original measure differential equation. This theorem generalizes a special result by Kurzweil [2] and a linear result by the author [5]. Sesekin [10] has proved an analogous theorem for a more restricted system in a wider class of regularizations.