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.