In this paper, the following third-order nonlinear delay differential equation with periodic coefficients x′′′(t) + p(t)x′′(t) + q(t)x′(t) + r(t)x(t) = f (t, x (t) , x(t− τ(t))) + c(t)x′(t− τ(t)), is considered. By employing Green’s function and Krasnoselskii’s fixed point theorem, we state and prove the existence of positive periodic solutions to the third-order delay differential equation.

This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations. Systemtheoretic results are provided for both classes of systems (among them converse Lyapunov results). The proposed framework can allow the study of discontinuous solutions for nonlinear systems described by a sing...

the aim of the present paper is the investigation of some problems which can be reduced to thegoursat problem for a third order equation. some results and theorems are given concerning the existence anduniqunce for solving the suggested problem.

It is demonstrated that the method of steps for linear delay-differential equation together with the inverse Laplace transform can be used to find a converging sequence of polynomial approximants to the transcendental function determining stability of the delay equation. Numerical stability charts are shown to illustrate convergence. This approach can serve as a basis for an efficient numerical...

In this work, we successfully extended one-dimensional differential transform method (DTM), by presenting and proving some theorems, to solving nonlinear high-order multi-pantograph equations. This technique provides a sequence of functions which converges to the exact solution of the problem. Some examples are given to demonstrate the validity and applicability of the present method and a comp...

Based on Riccati transformation and the inequality technique, we establish some new sufficient conditions for oscillation of the second-order neutral delay dynamic equations on time scales. Our results not only extend and improve some known theorems, but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation ...

This paper is concerned with the oscillation of certain third-order nonlinear delay differential equations with damping. We give new characterizations of oscillation of the third-order equation in terms of oscillation of a related, well-studied, second-order linear differential equation without damping. We also establish new oscillation results for the third-order equation by using the integral...

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...