Document Type
Report
Source Publication Title
Technical Report 63
Abstract
In this paper we prove the existence of solutions to nonlinear Volterra integral equations in a Banach Space. A comparison theorem and the existence of maximal solutions are also obtained using the notion of ordering with respect to a cone. As is known, in infinite dimensional Banach spaces compactness-type conditions are needed to prove existence, whereas in finite dimensional cases these assumptions are not necessary. The results of the paper generalize the corresponding results of Nohel [6]. See also Miller [5] and Lakshmikantham and Leela [2]. Throughout this paper, E will denote a Banach space, and [to,to + a] = J C R. We also use Be(xo) to denote the ball of radius centered at xo , i.e., [see pdf for notation]. The equation under consideration is(1.1) [see pdf for notation] where ^ C E open, xo :J ^ ^ and K:J x J x ^ ^ E.
Disciplines
Mathematics | Physical Sciences and Mathematics
Publication Date
5-1-1977
Language
English
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Vaughn, Randy, "Existence and Comparison Results for Nonlinear Volterra Integral Equations in a Banach Space" (1977). Mathematics Technical Papers. 238.
https://mavmatrix.uta.edu/math_technicalpapers/238