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.

The best ebooks about Periodic Solutions Of First Order Functional Differential Equations In Population Dynamics that you can get for free here by download this Periodic Solutions Of First Order Functional Differential Equations In Population Dynamics and save to your desktop. This ebooks is under topic such as communications in applied analysis 12 multiple periodic positive periodic solutions ...

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...

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.

In this paper, the C-conforming finite element method is analyzed for a class of nonlinear fourth-order hyperbolic partial differential equation. Some a priori bounds are derived using Lyapunov functional, and existence, uniqueness and regularity for the weak solutions are proved. Optimal error estimates are derived for both semidiscrete and fully discrete schemes. Keywords—Nonlinear fourth-ord...