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.

In this paper we deal with differential equations of the form yy ' = P(x, y) where y ' = dy/dx and P(x, y) is a polynomial in the variables x and y of degree n in the variable y. We provide an upper bound for the number ...

We prove a periodic averaging theorem for generalized ordinary differential equations and show that averaging theorems for ordinary differential equations with impulses and for dynamic equations on time scales follow easily ...

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 paper we present the main results of the master thesis in applied mathematics of the second named author, which was supervised by the first named author. Such results, and for instance this paper, concerns to ...

We present a sufficient condition for a zero of a function that arises typically as the characteristic equation of a linear functional differential equations of neutral type, to be simple and dominant. This knowledge is ...

In this article the numerical approximation of the stochastic transport equation is considered. We propose a new computational scheme for the effective simulation of the solutions of this equation. Results on the convergence ...

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 ...