Systems described by Volterra type integral operators

Abstract

In the paper some sufficient condition for the nonlinear integral operator of the Volterra type to be a diffeomorphism defined on the space of absolutely continuous functions are formulated. The proof relies on consideration of the linearized equation together with Palais-Smale condition, thus a combination of topological and variational methods is used. The applications of the result to the control systems with feedback and to the specific nonlinear Volterra equation are presented.