Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 39, pp. 1-9.
Title: Nonlinear Volterra integral equations in Henstock
integrability setting
Author: Bianca-Renata Satco (Univ. of Suceava, Romania)
Abstract:
We prove the existence of global solutions for nonlinear
Volterra-type integral equations involving the Henstock integral
in Banach spaces. The functions governing the equation are supposed
to be continuous only with respect to some variables and to
satisfy some integrability or boundedness conditions.
Our result improves the similar one given in [16]
(where uniform continuity was required), as well as those referred
therein. Then a related existence result is deduced in the
set-valued case.
Submitted January 29, 2008. Published March 14, 2008.
Math Subject Classifications: 45D05, 26A39, 47H10.
Key Words: Nonlinear Volterra equation; Henstock integral;
Darbo's fixed point theorem.