Document Type
Report
Source Publication Title
Technical Report 114
Abstract
The study of Cauchy problem for ordinary differential equations in a Banach space has been extensive [2,4,10]. It is of interest to look at the corresponding problem for delay differential equations since such equations occur in many physical problems. Existence of solutions of such equations are considered in [6,8,9] using monotonicity conditions and dissipative conditions.In this paper our objective is to prove the existence of extremal solutions for the delay differential equation [see pdf for notation] (1.1) relative to a cone k of the Banach space E. For this purpose, we begin by proving an existence result under a simple set of conditions without assuming uniform continuity on f we then develop needed theory of differential inequalities and utilize this to show the existence of extremal solutions for (1.1) Several useful comparison theorems are then proved including a flow invariance result. Our results generalize some of the recent results for equations without delay [5,7].
Disciplines
Mathematics | Physical Sciences and Mathematics
Publication Date
10-1-1979
Language
English
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Laughn, R. L. and Vatsala, A. S., "Existence of Extremal Solutions and Comparison Results for Delay Differential Equations in Abstract Cones" (1979). Mathematics Technical Papers. 135.
https://mavmatrix.uta.edu/math_technicalpapers/135