Stability of solutions of systems of Volterra integral equations

Abstract

In this paper we propose new sufficient conditions for stability of solutions of systems of Volterra linear integral equations and systems of linear integro-differential Volterra equations. Solution stability conditions for systems of Volterra linear integral equations are studied with perturbed right hand sides of the equations. These new sufficient conditions are expressed in terms of logarithmic norms of matrices consisting of coefficients of equations and derivatives of their kernels. For integro-differential Volterra equations we also provide sufficient conditions for stability of solutions when the initial conditions are perturbed.