WEIGHTED PSEUDO ALMOST-PERIODIC SOLUTIONS OF SHUNTING INHIBITORY CELLULAR NEURAL NETWORKS WITH MIXED DELAYS

In this paper, we prove the existence and the global exponential stability of the unique weighted pseudo almost-periodic solution of shunting inhibitory cellular neural networks with mixed time-varying delays comprising different discrete and distributed time delays. Some sufficient conditions are given for the existence and the global exponential stability of the weighted pseudo almost-periodic solution by employing fixed point theorem and differential inequality techniques. The results of this paper complement the previously known ones. Finally, an illustrative example is given to demonstrate the effectiveness of our results.

Weighted Pseudo Almost Periodic Solutions of N-th Order Neutral Differential Equations with Piecewise Constant Arguments

In this work, we present some existence theorems of weighted pseudo almost periodic solutions for N-th order neutral differential equations with piecewise constant argument by means of weighted pseudo almost periodic solutions of relevant difference equations.

Pseudo Almost Periodic Solutions of a Singularly Perturbed Differential Equation with Piecewise Constant Argument

Under suitable assumptions, the existence and the uniqueness of the pseudo-almost periodic solution for a singularly perturbed differential equation with piecewise constant argument are obtained. In addition, the stability properties of these solutions are characterized by the construction of manifolds of initial data.

The Existence of Pseudo-almost Periodic Solutions of Third-order Neutral Differential Equations with Piecewise Constant Argument

In this paper, we present some existence theorems for pseudo-almost periodic solutions of differential equations with piecewise constant argument by means of pseudo-almost periodic solutions of relevant difference equations.

Weighted Pseudo Asymptotically Periodic Mild Solutions of Evolution Equations

In this paper, we propose a new class of functions called weighted pseudo S-asymptotically periodic function in the Stepanov sense and explore its properties in Banach space including composition theorems. Furthermore, the existence, uniqueness of the weighted pseudo S-asymptotically periodic mild solutions to partial evolution equations and nonautonomous semilinear evolution equations are investigated. Some interesting examples are presented to illustrate the main findings.

PSEUDO-ALMOST PERIODIC SOLUTIONS TO SOME FUNCTIONAL DIFFERENTIAL EQUATIONS

This paper is concerned with the pseudo-almost periodic solutions to some functional differential equations. By the exponential dichotomy theory and Schauder’s fixed-point theorem, some results on the existence and uniqueness of pseudo-almost periodic solutions to the system are obtained.

A new almost periodic type of solutions of second order neutral delay differential equations with piecewise constant argument

A definition of pseudo almost periodic sequence is given and the existence of pseudo almost periodic sequence to difference equation is studied. Based on these, the existence of pseudo almost periodic solutions to neutral delay differential equations with piecewise constant argument is investigated

On a new almost periodic type solution of a class of singularly perturbed differential equations with piecewise constant argument

A new class of ergodic sequences, pseudo almost periodic sequence, is introduced, and the existence of pseudo almost periodic sequence to difference equation is studied. Based on these, we investigate the existence of pseudo almost periodic solutions for a nonautonomous, singularly perturbed differential equations with piecewise constant argument.

A New Almost Periodic Type Solution of First Order Neutral Delay Differential Equations with Piecewise Constant Argument

In this paper,we introduce a new class of ergodic sequences,pseudo almost periodic sequences,and study the existence of pseudo almost periodic sequences to difference equations.On the basis of these,we investigate the existence of pseudo almost periodic solutions for neutral delay differential equations with piecewise constant argument, d/(dt)(y(t)+py(t-1))=qy(2[(t+1)/2])+g(t,y(t),([t])).

受迫摆方程的伪概周期解

利用伪概周期函数的性质和Banach压缩映像原理研究受迫摆方程的伪概周期解问题,证明伪概周期解的存在性及在条件‖y-π‖L∞<π2下的唯一性。

具可变时滞和分布时滞的细胞神经网络的2~N具权重伪概周期解问题(英文)

本文讨论一类具可变时滞和分布时滞的细胞神经网络的2 N具权重伪概周期解的存在性和多重性.通过对系统功能函数和参数给出一些新的假设,把细胞神经网络的不变盆分成2 N个紧凸子集.证明过程说明在每一个紧凸子集内至少存在该系统的一个具权重伪概周期解.最后给出一个例子说明所得结果的可行性.

具有逐段常变量神经网络系统的伪概周期解

结合生物模型,针对一类具有逐段常变量神经网络系统的伪概周期解的存在性问题,利用伪概周期函数的等价定义、相关性质以及相应的差分方程进行了研究.依据逐段常变量微分方程的解在一点的连续性,构造了一个差分方程,利用差分方程的伪概周期序列解以及方程中有关函数给出了这类微分方程的伪概周期解存在的充分条件.此类神经网络系统结合了微分方程和差分方程的性质,可应用到模式识别、信号处理、联想记忆等方面.

具逐段常变量的中立型时滞微分方程的伪概周期解

通过构造二阶差分方程的伪概周期序列解 ,研究了带逐段常变量的中立型时滞微分方程ddt(y(t) +py(t - 1) ) =a0 y([t]) +a1y([t- 1]) +F(t,y(t) ,y([t]) )

共振条件下一类时滞微分方程周期解的多解性

应用临界点理论中的伪几何指标理论,研究时滞微分方程.x(t)=-f(x(t),x(t-π2))的周期解的存在性.研究了当f在无穷远处共振时,方程存在多个周期解的若干充分条件,与已有的用分析的技巧来寻找伴随的平面常微分系统的周期解的方法比较,该方法适合更高维的情形,为以后研究此类方程提供了一个新的工具.

具分布时滞的C-G神经网络模型的伪概周期解

利用不动点定理和不等式分析技巧,讨论了一类分布时滞C-G神经网络,得到了其伪概周期解存在且唯一的一个新的充分条件,并给出一个实例来说明我们结果的正确性.

一类Lasota-Wazewska模型伪概周期解的全局吸引性

Lasota-Wazewska模型常被用来描述动物体内红血球的再生情况.基于Banach压缩映射原理同时构造合适的Lyapunov函数,针对一类带时滞的Lasota-Wazewska模型研究了其伪概周期解的存在性、唯一性及全局吸引性.该文结果具有一定的优越性,且能够使关于Lasota-Wazewska模型动力学行为的刻画更加丰富.

一类半线性微分方程的调和伪概周期解

利用不动点理论,给出了一类半线性微分方程有界的调和伪概周期解存在的充分条件.

一类广义摆方程的伪概周期解

利用伪概周期函数的性质和Banach压缩映像原理研究了一类广义摆方程的伪概周期解问题,证明了该伪概周期解的存在性及在‖u-π‖L∞<π/2中的唯一性.

一类时滞摆方程的伪概周期解

利用伪概周期函数的性质和Banach压缩映像原理,研究了一类常见时滞摆方程的伪概周期解问题,证明了该伪概周期解的存在性及在‖u‖L∞<1中的唯一性。

抽象泛函微分方程的权伪概周期解(英文)

本文利用算子半群理论和Banach不动点定理研究了一类具非局部条件的抽象泛函微分方程权伪概周期解的存在唯一性,所得结论拓展了已有结果.