We study travelling kinks in the spatial discretizations of the nonlinear Klein–Gordon equation, which include the discrete φ lattice and the discrete sine–Gordon lattice. The differential advance-delay equation for travelling kinks is reduced to the normal form, a scalar fourth-order differential equation, near the quadruple zero eigenvalue. We show numerically non-existence of monotonic kinks...

We consider a certain second-order nonlinear delay differential equation and prove that the all solutions oscillate when proper impulse controls are imposed. An example is given. c © 2006 Elsevier Science Ltd. All rights reserved. Keywords—Delay differential equations, Second-order, Nonlinear, Oscillation, Impulses.

This study focuses on studying an oscillation of a second-order delay differential equation. Start work, the equation is introduced here with adequate provisions. All previous braced by theorems and examplesthat interpret applicability firmness acquired provisions

In this paper, we study the instability of the zero solution to a nonlinear differential equation with variable delay. By using the Lyapunov functional approach, some sufficient conditions for instability of the zero solution are obtained. Keywords—Instability, Lyapunov-Krasovskii functional, delay differential equation, fifth order.

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A partial differential equation with the argument [Z.t] is studied, where [.] denotes the greatest integer function. The infinite delay -[Zt] leads to difference equations of unbounded order. KEY WORDSAND PHRASES. Partial differential equation, piecewise constant delay, boundary value problem, initial value problem. 1991 AMS SUBJECT SIFICATION CODE. 35A05, 35B25, 35L10, 34K25.

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))) + d dt g (t, x (t− τ (t))) , is considered. By employing Green’s function, Krasnoselskii’s fixed point theorem and the contraction mapping principle, we state and prove the existence and uniqueness of periodic solutions...