Nonlinear Volterra integral equations in Henstock integrability setting

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.

Keywords

• Nonlinear Volterra equation
• Henstock integral
• Darbo's fixed point theorem