Displaying similar documents to “Global Existence and Stability for Neutral Functional Evolution Equations with State-Dependent Delay”

Resolvent of nonautonomous linear delay functional differential equations

Joël Blot, Mamadou I. Koné (2015)

Nonautonomous Dynamical Systems

Similarity:

The aim of this paper is to give a complete proof of the formula for the resolvent of a nonautonomous linear delay functional differential equations given in the book of Hale and Verduyn Lunel [9] under the assumption alone of the continuity of the right-hand side with respect to the time,when the notion of solution is a differentiable function at each point, which satisfies the equation at each point, and when the initial value is a continuous function.

Nonautonomous partial functional differential equations; existence and regularity

Moussa El-Khalil Kpoumiè, Khalil Ezzinbi, David Békollè (2017)

Nonautonomous Dynamical Systems

Similarity:

The aim of this work is to establish several results on the existence and regularity of solutions for some nondensely nonautonomous partial functional differential equations with finite delay in a Banach space. We assume that the linear part is not necessarily densely defined and generates an evolution family under the conditions introduced by N. Tanaka.We show the local existence of the mild solutions which may blow up at the finite time. Secondly,we give sufficient conditions ensuring...

A Lyapunov functional for a system with a time-varying delay

Józef Duda (2012)

International Journal of Applied Mathematics and Computer Science

Similarity:

The paper presents a method to determine a Lyapunov functional for a linear time-invariant system with an interval timevarying delay. The functional is constructed for the system with a time-varying delay with a given time derivative, which is calculated on the system trajectory. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.

Characterization of shadowing for linear autonomous delay differential equations

Mihály Pituk, John Ioannis Stavroulakis (2025)

Czechoslovak Mathematical Journal

Similarity:

A well-known shadowing theorem for ordinary differential equations is generalized to delay differential equations. It is shown that a linear autonomous delay differential equation is shadowable if and only if its characteristic equation has no root on the imaginary axis. The proof is based on the decomposition theory of linear delay differential equations.