Functional Differential Inequality Research Articles

Positive almost periodic solutions for shunting inhibitory cellular neural networks with time-varying delays

This paper is concerned with the existence and exponential stability of positive almost periodic solutions of shunting inhibitory cellular neural networks (SICNNs) with time-varying delays arising from the description of the states of neurons in delayed neural networks in a time-varying situation. By applying Lyapunov functional method and differential inequality techniques, new sufficient conditions ensuring the existence and exponential stability of positive almost periodic solutions for SICNNs are established.

Exponential convergence for a class of delayed cellular neural networks with time-varying coefficients

In this Letter, we consider a class of delayed cellular neural networks with time-varying coefficients. By applying Lyapunov functional method and differential inequality techniques, we establish new results to ensure that all solutions of the networks converge exponentially to zero point.

Existence and exponential stability of almost-periodic solutions for high-order Hopfield neural networks

In this paper high-order Hopfield neural networks (HHNNs) with continuously distributed delays are considered. Several sufficient conditions for the existence and exponential stability of the almost-periodic solutions are established by using a fixed point theorem, Lyapunov functional method and differential inequality techniques. The results of this paper are new and complement previously known ones.

Distribution of zeros of solutions of functional differential equations

By improving the bracketing techniques for a functional differential inequality in a previous paper [H.W. Wu, Y.T Xu, The distribution of zeros of solutions of neutral differential equations, Appl. Math. Comput. 156 (3) (2004) 665–677], we are able to derive sharper upper bounds on the distance between zeros of solutions of a class of neutral functional differential equations with delays, and hence improve many known bounds in the literature.

Differential inequalities for a nonsmooth value functional in control systems with an aftereffect

Functional differential inequalities, uniquely describing the optimal guaranteed result, are obtained for a control system with aftereffect, in the presence of disturbances. Specific forms of these inequalities are given for typical particular cases.

On the Cauchy type problem for systems of functional differential equations

Using theorems on functional differential inequalities, we establish new efficient conditions for the solvability as well as unique solvability of the Cauchy type problem for systems of functional differential equations in both linear and nonlinear cases.

Almost periodic solutions for shunting inhibitory cellular neural networks without global Lipschitz and bounded activation functions

In this Letter the shunting inhibitory cellular neural networks (SICNNs) with time-varying delays are considered. Without assuming the global Lipschitz and bounded conditions of activation functions, some sufficient conditions for the existence and local exponential stability of the almost periodic solutions are established by using the fixed point theorem, Lyapunov functional method and differential inequality techniques. The results of this Letter are new and complement previously known results.

On Systems of Linear Functional Differential Inequalities

Abstract The Cauchy problem for 𝑛-dimensional systems of linear functional differential equations is studied. Some new theorems on systems of functional differential inequalities are established.

Existence and exponential stability of almost periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays☆

Abstract In this paper, the shunting inhibitory cellular neural networks (SICNNs) with continuously distributed delays are considered. Sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using fixed point theorem, Lyapunov functional method and differential inequality techniques.

Almost periodic solutions for shunting inhibitory cellular neural networks without global Lipschitz activation functions

In this paper the shunting inhibitory cellular neural networks (SICNNs) with continuously distributed delays are considered. Without assuming the global Lipschitz conditions of activation functions, sufficient conditions for the existence and local exponential stability of the almost periodic solutions are established by using a fixed point theorem, Lyapunov functional method and differential inequality techniques. The results of this paper are new and they complement previously known results.

EXISTENCE AND EXPONENTIAL STABILITY OF ALMOST PERIODIC SOLUTIONS FOR CELLULAR NEURAL NETWORKS WITH CONTINUOUSLY DISTRIBUTED DELAYS

In this paper cellular neural networks with continuously distributed delays are considered. Sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using fixed point theorem, Lyapunov functional method and differential inequality technique. The results of this paper are new and they complement previously known results.

Functional differential inequalities with unbounded delay

Functional differential inequalities with unbounded delay

Existence and exponential stability of almost periodic solutions for cellular neural networks with mixed delays

Abstract In this paper cellular neural networks with mixed delays are considered. Sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using fixed point theorem, Lyapunov functional method and differential inequality technique. The results of this paper are new and they complement previously known results.

Existence and stability of almost periodic solutions for shunting inhibitory cellular neural networks with time-varying delays

Abstract In this paper, the shunting inhibitory cellular neural networks (SICNNs) with time-varying delays are considered. Sufficient conditions for the existence and local exponential stability of the almost periodic solutions are established by using fixed point theorem, Lyapunov functional method and differential inequality techniques. The results of this paper are new and they complement previously known results.

Existence and stability of almost periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays

In this Letter the shunting inhibitory cellular neural networks (SICNNs) with continuously distributed delays are considered. Sufficient conditions for the existence and local exponential stability of the almost periodic solutions are established by using fixed point theorem, Lyapunov functional method and differential inequality techniques. The results of this Letter are new and they complement previously known results.

Functional Differential Inequalities with Unbounded Delay

Abstract We prove that a function of several variables satisfying a functional differential inequality with unbounded delay can be estimated by a solution of a suitable initial problem for an ordinary functional differential equation. As a consequence of the comparison theorem we obtain a Perron-type uniqueness result and a result on continuous dependence of solutions on given functions for partial functional differential equations with unbounded delay. We consider classical solutions on the Haar pyramid.

Abstract differential inequalities and the Cauchy problem for infinite-dimensional linear functional differential equations

We establish optimal, in a sense, unique solvability conditions of the Cauchy problem for a wide class of linear functional differential equations in a Banach space with a solid wedge. The conditions are formulated in terms of certain abstract functional differential inequalities.

Comparison Method of Stability Analysis of Semilinear Time-Delay Stochastic Evolution Equation

In this paper, we set up the comparison theorem between the mild solution of semilinear time-delay stochastic evolution equation with general time-delay variable and the solution of a class (1-dimension) deterministic functional differential equation, by using the Razumikhin–Lyapunov type functional and the theory of functional differential inequalities. By applying this comparison theorem, we give various types of the stability comparison criteria for the semilinear time-delay stochastic evolution equations. With the aid of these comparison criteria, one can reduce the stability analysis of semilinear time-delay stochastic evolution equations in Hilbert space to that of a class (1-dimension) deterministic functional differential equations. Furthermore, these comparison criteria in special case have been applied to derive sufficient conditions for various stability of the mild solution of semilinear time-delay stochastic evolution equations. Finally, the theories are illustrated with some examples.

The oscillation of hyperbolic functional differential equations

This paper, deals with the oscillation properties of a class of hyperbolic functional differential equations and obtains a set of criterions, by using some results of functional differential inequality. These results reveal that the vary difference between hyperbolic functional differential equations and hyperbolic differential equations.

Oscillation criteria for a class of partial functional‐differential equations of higher order

Higher order partial differential equations with functional arguments including hyperbolic equations and beam equations are studied. Sufficient conditions are derived for every solution of certain boundary value problems to be oscillatory in a cylindrical domain. Our approach is to reduce the multi‐dimensional oscillation problem to a one‐dimensional problem for higher order functional differential inequalities.