Boundedness of solutions of matrix nonlinear volterra difference equations

Abstract

Nonlinear discrete-time Volterra equations in a Euclidean space are considered. Conditions for the boundedness of solutions are established by virtue of recent estimates for the norm of the resolvent of Volterra operators. The conditions are formulated in the terms of coefficients of considered equations. In addition, estimates for the c0- and l2-norms of solutions are derived.