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Existence and Comparison Results for Nonlinear Volterra Integral Equations in a Banach Space

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Existence and Comparison Results for Nonlinear Volterra Integral Equations in a Banach Space

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Title: Existence and Comparison Results for Nonlinear Volterra Integral Equations in a Banach Space
Author: Vaughn, Randy
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.
URI: http://hdl.handle.net/10106/2282
Date: 1977-05

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