Global Solutions for Volterra Ordinary and Retarded Integral Equations

Abstract

Abstract. Using a generalization of Darbo's fixed point theorem, we obtain the existence of global solutions for nonlinear Volterra-type integral equations in Banach spaces. The involved functions are supposed to be continuous only with respect to some variables, integrability or essential boundedness conditions being also imposed. Our result improves the similar result given in [10] (where uniform continuity was required), as well as those referred by the authors of the cited paper. Finally, following the same ideas, the existence of continuous solutions is proved for a Volterra-type retarded integral equation, under less restrictive assumptions than in the others related results in literature. IntroductionThe importance of Volterra-type integral equations in solving various nonlinear problems in science determined many authors to study the existence of (continuous or better) solutions (see e.g. The setting is that of a separable Banach space and the assumptions made on the operators are much weaker than those made by the previously cited 2000 Mathematics Subject Classification: 45D05, 47H10, 49K25.