Estimates for Solutions of One Class of Nonlinear Neutral Type Systems with Several Delays

Abstract

We consider a class of systems of nonlinear differential equations of neutral type with several delays. We obtain conditions of exponential stability of the zero solution and establish estimates characterizing the exponential decay rate of solutions at infinity. Bibliography: 14 titles.We consider systems of differential equations with several delays of the formwhere D, A, and B j are constant n × n-matrices, τ j > 0 are the delay parameters, τ 1 > τ k , . . . , m, and F (t, u, v 1 , . . . , v m ) is a real-valued continuous vector-valued function satisfying the Lipschitz condition with respect to u and the inequalityIn the case D = 0, systems of the form (1) are referred to as neutral type systems [1].