Nonlinear Volterra integral equations in Henstock integrability setting. (English) Zbl 1169.45300

Satco, Bianca-Renata

Electron. J. Differ. Equ. 2008, Paper No. 39, 9 p. (2008).

Summary: 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 by L. Liu, F. Gei, C. Wu, Y. Wu [J. Math. Anal. Appl. 309, No. 2, 638–649 (2005; Zbl 1080.45005)] (where uniform continuity was required), as well as those referred therein. Then a related existence result is deduced in the set-valued case.

MSC:

45D05	Volterra integral equations
26A39	Denjoy and Perron integrals, other special integrals
47H10	Fixed-point theorems

Keywords:

nonlinear Volterra equation; Henstock integral; Darbo’s fixed point theorem

Citations:

Zbl 1080.45005