In this paper we introduce a new class of abstract integral equations which enables us to study in a unified manner several different types of differential equations. (C) 2012 Elsevier Inc. All rights reserved.

By using the concept of integrable dichotomy, the fixed point theory, functional analysis methods and some new technique of analysis, we obtain new criteria for the existence and uniqueness of bounded and periodic solutions ...

We study the existence and uniqueness of mild and classical solutions for a general class of abstract impulsive differential equations with state-dependent impulses. Some examples on partial differential equations are presented.

In this note we study the existence of global solutions for a class of impulsive abstract differential equations with non-instantaneous impulses. Specifically, we establish the existence of mild solutions on and the existence ...

In this work we study the existence and regularity of mild solutions for a damped second order abstract functional differential equation with impulses. The results are obtained using the cosine function theory and fixed ...

In this paper we discuss the existence of mild, strict and classical solutions for a class of abstract integro-differential equations in Banach spaces. Some applications to ordinary and partial integro-differential equations ...

We study measure functional differential equations and clarify their relation to generalized ordinary differential equations. We show that functional dynamic equations on time scales represent a special case of measure ...

In this work, we establish the existence and uniqueness of antiperiodic solution for a class of nth-order functional differential equations with infinite delay. The main tool in our study is the coincidence degree theory. ...