Existence of Solutions in a Closed Set for Delay Differential Equations in Banach Spaces
Abstract
**Please note that the full text is embargoed** ABSTRACT: The study of the Cauchy problem for ordinary differential equations
in a Banach space has been extensive [1,3-7,9-12]. The two main directions that are followed in such a study are (i) finding monotonicity type conditions which guarantee the existence as well as uniqueness of solutions and (ii) finding compactness type conditions which assure only the existence
of solutions [3,4]. It is also known [10,12] that in order to prove the existence of solutions in a closed subset F of the Banach space, a boundary condition of the type [see pdf for notation] is required.