The current final project belongs to a subject in the master’s degree in Advanced Mathematics at the University of Barcelona. It deals with time delays which usually are arisen in differential equations. Firstly, the project develops the main important known results of Delay Differential Equations, which are a specific case of Functional Differential Equations. In particular, we shall also focu...

where W is a Wiener process, Z is a Hölder continuous process with Hölder exponent greater than 1/2, the coefficients a, b, c depend on the past of the process X . The integral with respect to W is understood in the usual Itô sense, while the one with respect to Z is understood in the pathwise sense. (A precise definition of all objects is given in Section 2.) We will call this equation a mixed...

This paper is concerned with the oscillatory behavior of first-order delay differential equations of the form x′(t) + p(t)x(τ(t)) = 0, t ≥ t0, (1) where p, τ ∈ C([t0,∞),R),R = [0,∞), τ(t) is non-decreasing, τ(t) < t for t ≥ t0 and limt→∞ τ(t) =∞. Let the numbers k and L be defined by

This paper is concerned with a class of linear impulsive delay differential equations. Asymptotic stability of analytic solutions of this kind of equations is studied by the property of delay differential equations without impulsive perturbations. New numerical methods for this kind of equations are constructed. The convergence and asymptotic stability of the methods for this kind of equations ...

Uncertain delay differential equation is a type of differential equations driven by a canonical Liu process. This paper mainly focuses on the stability of uncertain delay differential equations. At first, the concept of stability in measure, stability in mean and stability in moment for uncertain delay differential equations will be presented. In addition, the sufficient condition for uncertain...

In this paper we extend existing numerical methods for bifurca-tion analysis of delay diierential equations with constant delay towards equations with state-dependent delay. In particular, we study the computation, continuation and stability of steady state solutions and periodic solutions of such equations. We collect the relevant theory and point out open theoretical problems in the context o...

A semi-empirical mathematical model for predicting the physical part of ignition delay period in the combustion of diesel engines with swirl is developed. This model is based on a single droplet evaporation model. The governing equations, namely, equations of droplet motion, heat and mass transfer were solved simultaneously using a Runge-Kutta step by step method. The computation was executed u...