  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.
