This paper is devoted to the study of the class of continuous and bounded functions f : [0, ∞) → X for which exists ω > 0 such that lim t→∞ (f (t + ω) − f (t)) = 0 (in the sequel called S-asymptotically ω-periodic functions). We discuss qualitative properties and establish some relationships between this type of functions and the class of asymptotically ω-periodic functions. We also study the existence of S-asymptotically ω-periodic mild solutions of the first-order abstract Cauchy problem in Banach spaces.

This work is concerned with a class of quasi-linear partial neutral functional differential equations with unbounded delay. Specifically, we establish existence of mild and strong solutions for equations that can be described as an abstractis the infinitesimal generator of a strongly continuous semigroup of linear operators on a Banach space and F and G are appropriate functions defined on a phase space. ᮊ

This paper is concerned with partial neutral functional differential equations of first and second order with impulses. We establish some results of existence of mild solutions for these classes of equations.

In this article we establish a result of existence of periodic solutions for the class of quasi-linear partial neutral functional differential equations with unbounded delay that can be described as the abstract functional differential equation

Artículo de publicación ISIIn this paper we establish the existence of mild solutions for a non-autonomous abstract semi-linear second order differential equation submitted to nonlocal initial conditions. Our approach relies on the existence of an evolution operator for the corresponding linear equation and the properties of the Hausdorff measure of non-compactness.Partially supported by: CONICYT under grant FONDECYT 1130144 and DICYT-USACH, FONDECYT 1110090 and MECESUP PUC 0711