The Existence and Continuous Dependence Theorem for Solutions of Differential Equations

Abstract

The basic result of this chapter is formulated in Theorems 4.3 and 4.4 on the existence and continuous dependence of solutions of differential equations on the initial data and right-hand sides. These theorems are formulated and proved in Sections 4.4 and 4.5, and they appear as comparatively easy corollaries of Theorem 4.2 on the existence and continuous dependence of solutions of differential equations with fixed right-hand sides, which is proved in Section 4.3. The technique used for deriving Theorems 4.3 and 4.4 from Theorem 4.2 is standard, and it often turns out to be very useful.