Document Type


Source Publication Title

Technical Report 30


Recent interest in the Cauchy problem for differential equations in a Banach space [9] has stimulated a similar interest for differential equations of a retarded type in a Banach space. The difficulty in imposing assumptions due to a different range and domain space has been overcome in [4] where existence of solutions is established using a monotoni- city type condition in terms of norm and weaker forms of differential inequalities. The theory of existence of solutions of differential equations has been used in [1,2,5,6,7] to obtain existence of zeros and fixed points for nonlinear operators from E into E. In this paper we consider the existence of zeros of operators which map into E but whose domain is the space of continuous functions on some real interval into E. Since such operators generate differential equations of retarded type, we call such operators retarded type. We employ generalized inner product [1,6] and adapt the methods analogous to [1,2,7]. Our results generalize those of [4]. Furthermore, we obtain for the first time, existence of zeros of operators of retarded type.


Mathematics | Physical Sciences and Mathematics

Publication Date




Included in

Mathematics Commons



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.