具有时变时滞惯性四元Hopfield神经网络反周期解的动力学研究

周期性、反周期性和概周期性是时变神经网络的重要动态行为特性.本文在不将所研究的神经网络分解为实值系统的情况下,根据重合度理论中的延拓定理和不等式技巧,通过构造不同于现有平衡点稳定性研究的李雅普诺夫函数,研究了一类具有变时滞的惯性四元Hopfield神经网络的反周期解的动力学问题,给出了上述神经网络反周期解存在的一个新的判别条件.并通过构造李雅普诺夫函数论证了上述神经网络反周期解的指数稳定性.     

Weighted pseudo almost automorphic functions and WPAA solutions to semilinear evolution equations

In this paper, we reveal several basic properties about nonlinear vector-valued weighted pseudo almost automorphic functions, including equivalence, completeness, translation invariance, composition theorem, and convolution theorem of these functions. We also give some concrete examples to illustrate our results. Finally, we obtain a new existence theorem of nonlinear weighted pseudo almost automorphic solutions for semilinear evolution equations in Banach spaces.     

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.     

Existence of weighted pseudo almost periodic solutions to some classes of hyperbolic evolution equations

This paper is concerned with the study of weighted pseudo almost periodic solutions to some classes of hyperbolic differential equations. Upon making some suitable assumptions, the existence and uniqueness of a weighted pseudo almost periodic solution is obtained. To illustrate our main result, we study the existence of a weighted pseudo almost periodic solution to a system of partial differential equations arising in control systems described by abstract retarded functional-differential equations with feedback control.     

Weighted pseudo‐almost periodic functions on time scales with applications to cellular neural networks with discrete delays

In this paper, we first propose a concept of weighted pseudo‐almost periodic functions on time scales and study some basic properties of weighted pseudo‐almost periodic functions on time scales. Then, we establish some results about the existence of weighted pseudo‐almost periodic solutions to linear dynamic equations on time scales. Finally, as an application of our results, we study the existence and global exponential stability of weighted pseudo‐almost periodic solutions for a class of cellular neural networks with discrete delays on time scales. The results of this paper are completely new. Copyright © 2016 John Wiley & Sons, Ltd.     

2n阶微分方程反周期解的存在性与唯一性

In this paper, we study the anti-periodic solutions for 2n-th order differential equations. By using the Schauder＇s fixed point theorem, we present some new results about the existence and uniqueness of anti-periodic solutions for 2n-th order differential equations.     

Weighted Pseudo Almost Periodic Solutions for a Class of Hematopoiesis Model with Time-Varying Delay

In this paper, firstly, a notion of a class of generalized weighted pseudo al-most periodic function is introduced, then we investigate some basic and essential properties of the space that consists of these functions. Finally, we study the exis-tence of weighted pseudo almost periodic solutions to hematopoiesis model with time-varying delay.     

一类泛函微分方程反周期解的存在性

研究了一类含参泛函微分方程反周期解的存在性.获得了当参数在一定范围取值时反周期解的存在性结果,得到了反周期解存在的充分条件,并通过例子表明结果的可行性.主要工具为Leray-Schauder非线性抉择.     

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.     

On a Quasilinear Elliptic Equation with Superlinear Nonlinearities

This work is devoted to studying a quasilinear elliptic boundary value problem with superlinear nonlinearities in a weighted Sobolev space in a domain of $\mathbb{R}^{N}$. Based on the Galerkin method, Brouwer's theorem and the weighted compact Sobolev-type embedding theorem, a new result about the existence of solutions is revealed to the problem.     

Weighted pseudo almost periodic solutions of neutral functional differential equations

In this paper, we study weighted pseudo almost periodic solutions of neutral functional differential equations. By applying the properties of weighted pseudo almost periodic functions and the exponential dichotomy of linear systems as well as Krasnoselskii’s fixed point theorem, we establish the conditions for the existence of weighted pseudo-almost periodic solution of the equations.     

EXISTENCE AND UNIQUENESS OF ANTI-PERIODIC SOLUTIONS TO AN nTH-ORDER NONLINEAR DIFFERENTIAL EQUATION WITH MULTIPLE DEVIATING ARGUMENTS

In this paper,we use the Leray-Schauder degree theory to establish some new results on the existence and uniqueness of anti-periodic solutions to an nth-order nonlinear differential equation with multiple deviating arguments.     

一类具变参数的p-Laplacian中立型泛函微分方程反周期解的存在性

应用Leray Schauder 不动点定理,研究了一类具变参数的p-Laplacian中立型泛函微分方程(φp(x′(t)-c(t)x′(t-r)))′=f(x′(t))+β(t)g(x(t-τ(t)))+e(t)的反周期解问题,得到了反周期解存在的新的结果.     

关于长方矩阵的加权群逆的存在性

本文讨论长方矩阵的加权群逆．分别利用减逆和泛分解,给出了长方矩阵的加权群逆存在的几个充要条件以及加权群逆的计算公式．     

Anti-periodic solutions for a class of Liénard-type systems with continuously distributed delays

This paper considers the Liénard-type systems with continuously distributed delays. Some new sufficient conditions for the existence and exponential stability of the anti-periodic solutions are established.     

Pseudo almost periodic in distribution solutions to impulsive partial stochastic functional differential equations

In this paper, we study the piecewise pseudo almost periodicity in distribution for a stochastic process. Using the analytic semigroup theory and fixed point strategy with stochastic analysis theory, we obtain the existence and the exponential stability of piecewise pseudo almost periodic in distribution mild solutions for impulsive partial neutral stochastic functional differential equations under non-Lipschitz conditions. Moreover, an example is given to illustrate the general theorems.     

非自治中立型无穷时滞泛函微分方程的加权伪概自守解

首先引入h型Stepanov 加权伪概自守函数和∞型Stepanov加权伪概自守函数的概念, 接着建立了其函数空间的完备性以及相应组合定理, 最后证明了一类非自治无穷时滞偏中立型泛函微分方程在S^p-加权伪概自守系数下加权伪概自守解的存在唯一性.     

Stepanov-like pseudo almost periodic solutions for impulsive perturbed partial stochastic differential equations and its optimal control

This paper is mainly concerned with the Stepanov-like pseudo almost periodicity to a class of impulsive perturbed partial stochastic differential equations. Firstly, we prove the existence of $p$-mean piecewise Stepanov-like pseudo almost periodic mild solutions for the impulsive stochastic dynamical system in a Hilbert space under non-Lipschitz conditions. The results are obtained by using the fixed point techniques with fractional power arguments. Then the existence of optimal pairs of system governed by impulsive partial stochastic differential equations is also obtained. Finally, an example is provided to illustrate the developed theory.     

Weighted convergent and bounded solutions of vdterra difference systems with infinite delay

By using a weighted p-summable dichotomies and the contraction mapping principle we prove the existence of convergent and bounded solutions of Volterra difference equation with infinite delay