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.

15 pages

Cited by in corpus (2)

• Solvability of abstract semilinear equations by a global diffeomorphism theorem
• Global invertibility and implicit function theorems by mountain pass theorem