Stability of impulsive infinite delay differential equations

AbstractIn this work, we consider the stability of impulsive infinite delay differential equations. By using Lyapunov functions and the Razumikhin technique, we get some results that are more general than ones given before. And in using the Razumikhin technique, we use a new technique that has been given by Shunian Zhang; we extend this technique to study impulsive systems. An example is also discussed in this work to illustrate the advantage of the results obtained

Existence and continuous dependence of mild solutions for fractional abstract differential equations with infinite delay

In this paper, we prove the existence, uniqueness, and continuous dependence of the mild solutions for a class of fractional abstract differential equations with infinite delay. The results are obtained by using the Krasnoselskii's fixed point theorem and the theory of resolvent operators for integral equations

Solutions to non-autonomous integrodifferential equations with infinite delay

AbstractThe conclusions of Da Prato and Sinestrari concerning the non-autonomous evolution operator of hyperbolic type for the equationu′(t)=A(t)u(t)+f(t),t∈[0,T],u(0)=z are applied to find the uniqueness and existence of solution tou′(t)=A(t)u(t)+∫0tK(t,θ,u(θ))dθ+L(t)ut+f(t),t∈[0,T],u0=φ, where A(⋅) maybe nondensely defined. Moreover, some relative problems are concerned