Non-autonomous Neutral Functional Differential Equations Research Articles

Long-term behavior of nonautonomous neutral compartmental systems

The asymptotic behavior of the trajectories of compartmental systems with a general set of admissible initial data is studied. More precisely, these systems are described by families of monotone nonautonomous neutral functional differential equations with nonautonomous operator. We show that the solutions asymptotically exhibit the same recurrence properties as the transport functions and the coefficients of the neutral operator. Conditions for the cases in which the delays in the neutral and non neutral parts are different, as well as for other cases unaddressed in the previous literature are also obtained.

Periodicity of Solutions for Non-Autonomous Neutral Functional Differential Equations with State-Dependent Delay

Periodicity of Solutions for Non-Autonomous Neutral Functional Differential Equations with State-Dependent Delay

Asymptotic behavior of solutions of nonautonomous neutral dynamical systems

This paper studies the dynamics of families of monotone nonautonomous neutral functional differential equations with nonautonomous operator, of great importance for their applications to the study of the long-term behavior of the trajectories of problems described by this kind of equations, such us compartmental systems and neural networks among many others. Precisely, more general admissible initial conditions are included in the study to show that the solutions are asymptotically of the same type as the coefficients of the neutral and non-neutral part.

Stepanov-Almost Periodic Solutions of Non-autonomous Neutral Functional Differential Equations with Functional Delay

In this paper, we study the existence and uniqueness of Stepanov-almost periodic mild solution to the non-autonomous neutral functional differential equation $$\begin{aligned} \frac{{\hbox {d}}}{\hbox {d}t}[u(t)-F(t,u(t-\alpha (t)))]= & {} A(t)[u(t)-F(t,u(t-\alpha (t)))]\\&+\,G(t,u(t),u(t-\alpha (t))),\quad t\in \mathbb {R}, \end{aligned}$$ in a Banach space $$\mathbb {X},$$ where the family of linear operators A(t) satisfies the ‘Acquistapace–Terreni’ conditions, the evolution family generated by $$A(t),t\in \mathbb {R},$$ is exponentially stable, $$(\gamma -A(\cdot ))^{-1}$$ and $$\alpha (\cdot )$$ are almost periodic, and F and G are Stepanov-almost periodic continuous functions.

Periodic Solutions for Non-Autonomous Neutral Functional Differential Equations with Finite Delay

In this work, we study the existence of periodic solutions for some non-autonomous nonlinear partial functional differential equation of neutral type. We assume that the linear part is non-densely defined and generates an evolution family under the conditions introduced by N. Tanaka. The delayed part is assumed to be ω-periodic with respect to the first argument. Using a fixed-point theorem for multivalued mapping, some sufficient conditions are given to prove the existence of periodic solutions. An example is shown to illustrate our results.

Existence of Solutions for Abstract Non-Autonomous Neutral Differential Equations

AbstractIn this paper we discuss the existence of mild and classical solutions for a class of abstract non-autonomous neutral functional differential equations. An application to partial neutral differential equations is considered.

Global attracting set for a class of nonautonomous neutral functional differential equations

In this paper, a class of nonlinear and nonautonomous neutral functional differential equations is considered. By developing a new integral inequality, we obtain sufficient conditions for the existence of a global attracting set of neutral functional differential equations with time-varying delays. The results have extended and improved the related reports in the literature.

Exponential Ordering for Nonautonomous Neutral Functional Differential Equations

We study monotone skew-product semiflows generated by families of nonautonomous neutral functional differential equations with infinite delay and stable D-operator, when the exponential ordering is considered. Under adequate hypotheses of stability for the order on bounded sets, we show that the omega-limit sets are copies of the base to explain the long-term behavior of the trajectories. The application to the study of the amount of material within the compartments of a neutral compartmental system with infinite delay shows the improvement with respect to the standard ordering.

Infinite periodic and subharmonic solutions to a class of second-order nonlinear non-autonomous neutral functional differential equations

In this paper, by setting up a new Hilbert space H&#422γ τ and the variational method, we finded energy functions for a class of second-order nonlinear non-autonomous neutral functional differential equations. Then by critical point and Z2-group index theory, we get the sufficient condition for the existence of infinite periodic solutions for the system. Simultaneity, we put up an open question.

Periodic solutions of abstract neutral functional differential equations with infinite delay

We establish the existence of mild solutions and periodic mild solutions for a class of abstract first-order non-autonomous neutral functional differential equations with infinite delay in a Banach space.

Pseudo almost periodic solutions to some non-autonomous neutral functional differential equations with unbounded delay

In this paper we give some sufficient conditions, which ensure the existence of pseudo almost periodic solutions to some classes of non-autonomous first-order partial neutral functional-differential with unbounded delay.

A semigroup approach to nonlinear nonautonomous neutral functional differential equations

A class of nonlinear nonautonomous neutral functional differential equations is studied by associating with it an evolution equation in the space of initial data, the space W 1,1. Existence and regularity results are proved.

Coincidence degree and periodic solutions of neutral equations

The problem of existence of periodic solutions for some nonautonomous neutral functional differential equations is examined. It is an application of a basic theorem on the Fredholm alternative for periodic solutions of some linear neutral equations and of a generalized Leray-Schauder theory. Although proofs are simple, the results are nontrivial extensions to the neutral case of existence theorems for periodic solutions of functional differential equations.