Mild solutions for perturbed evolution equations with infinite state-dependent delay

Existence of Mild Solutions for Nonlocal Cauchy Problem for Fractional Neutral Evolution Equations with Infinite Delay

In this article, we study the existence of mild solutions for nonlocal Cauchy problem for fractional neutral evolution equations with infinite delay. The results are obtained by using the Banach contraction principle. Finally, an application is given to illustrate the theory. Full text

Existence and uniqueness of solutions for neutral periodic integro-differential equations with infinite delay

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Bounded and periodic solutions of infinite delay evolution equations

For A(t) and f (t, x, y) T -periodic in t , we consider the following evolution equation with infinite delay in a general Banach space X: u′(t)+A(t)u(t)= f (t, u(t), ut ), t > 0, u(s)= φ(s), s 0, (0.1) where the resolvent of the unbounded operator A(t) is compact, and ut (s) = u(t + s), s 0. By utilizing a recent asymptotic fixed point theorem of Hale and Lunel (1993) for condensing operators t...

Existence of the Mild Solutions for Impulsive Fractional Equations with Infinite Delay

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.