Stability Properties of a Discretized Neutral Delay Differential Equation

Stability of a critical nonlinear neutral delay differential equation

This work deals with a scalar nonlinear neutral delay differential equation issued from the study of wave propagation. A critical value of the coefficients is considered, where only few results are known. The difficulty follows from the fact that the spectrum of the linear operator is asymptotically closed to the imaginary axis. An analysis based on the energy method provides new results about ...

Stability of the Discretized Pantograph Differential Equation

In this paper we study discretizations of the general pantograph equation y'(t) = ay(t) + by(6(t)) + cy'((t)), f>0, y(0)=y0, where a , b , c , and yo are complex numbers and where 9 and <¡> are strictly increasing functions on the nonnegative reals with 0(0) = <^>(0) = 0 and 8(t) < t, 4>(t) < t for positive /. Our purpose is an analysis of the stability of the numerical solution with trapezo...

A Discretized Lyapunov Functional Approach to Stability of Linear Delay-differential Systems of Neutral Type

This paper considers the stability problem of linear delay-differential systems of neutral type. A discretized Lyapunov functional approach is developed. The resulting stability criteria are formulated in the form of a linear matrix inequality. For nominal systems, the analytical results can be approached with fine discretization. For uncertain systems, the new approach is much less conservativ...

Periodic solutions of a discretized differential delay equation

Positive Solutions of Neutral Delay Differential Equation

Neutral delay differential equations contain the derivative of the unknown function both with and without delays. Some new phenomena can appear, hence the theory of neutral delay differential equations is even more complicated than the theory of non-neutral delay equations. The oscillatory behavior of the solutions of neutral systems is of importance in both the theory and applications, such as...