On the asymptotic behavior of delay differential equations and its relationship with C0- semigoup

Abstract

In this paper, we study the asymptotic behavior of linear differential equations under nonlinear perturbation. Let’s consider the delay differential equations: dx dt = Ax + f(t, xt), where t 2 R+,A 2 L(E), f : R+ ×E −! E and (T(t))t 0 is C0-semigroup be generated by A. We will give some sufficient conditions for uniformly stable and asymptotic equivalence of above equations.