The Carathéodory and Plis–Davy Theorems, Krasovsky Regularization, and Continuous Dependence of Solutions on Parameters on the Right-Hand Side

Abstract

We weaken the assumptions of the classical Carathéodory and Plis–Davy theorems. We prove theorems on continuous dependence of solutions on parameters on the right-hand side and their corollaries generalizing the known results of the classical theory. Based on the axiomatic theory of ordinary differential equations, we expand the theorem on continuous dependence of solutions on parameters on the right-hand side to a larger class of differential equations and inclusions.