A GENERALIZATION OF ASCOLI-ARZELA THEOREM WITH AN APPLICATION

Abstract

In this paper, a set of C^m-smooth function from infinite interval [a,infty) to a Banach space is investigated. We obtain a su±cient and necessary condition to distinguish its relative compactness, which extends the well known Ascoli-Arzela's Theorem. As an application, we prove an existence theorem of solution for a class of second order boundary value problems in Banach spaces.