Extension of Peano’s Existence Theorem For A Second Order Initial Value Problem

Abstract

Several existence theorems are known for a first order Initial Value Problem (IVP). In this paper we extend the existence of Peano’s theorem to a second order Initial Value Problem ([6], [7]) of the type , by suitably constructing a sequence which is equicontinuous and uniformly bounded, so as to apply Ascoli-Arzela theorem.