On the asymptotic equilibrium and asymptotic equivalence of differential equations in Banach spaces

Abstract

We present some conditions for the asymptotic equilibrium of nonlinear differential equations and, in particular, a linear inhomogeneous equation in Banach spaces. We also discuss analogous problems for a linear equation with unbounded operator. Some obtained results are applied to problems of asymptotic equivalence.Hanoi, Vietnam.

Asymptotic equilibrium of integro-differential equations with infinite delay

“…In this paper, we extend the results in [1] to a class of integro-differential equations with infinite delay in a Hilbert space H which has the following form:…”

“…The asymptotic equilibrium problems of ordinary differential equations in a Banach space have been considered by several authors, Mitchell and Mitchell [3], Bay et al [1], but the results for the asymptotic equilibrium of integrodifferential equations with infinite delay still is not presented. In this paper, we extend the results in [1] to a class of integro-differential equations with infinite delay in a Hilbert space H which has the following form:…”