Asymptotic behaviour of solutions of the difference Schrödinger equation

We use the method of averaging and the discrete analogue of Levinson's theorem to construct the asymptotics for solutions of the difference Schrödinger equation. Moreover, we present the general form for the averaging change of variable.     

中立型抛物方程解的振动性与渐近性

本文研究了,具有分布滞量的非线性中立型抛物方程（E）解的振动性与渐近性,我们的结果推广了Bainov和Petrov[1]对方程的一些结果。     

Hille and Nehari type criteria for third-order delay dynamic equations

The objective of this note is to present new Hille and Nehari type asymptotic criteria for a class of third-order delay dynamic equations on a time scale. Assumptions in our theorems are less restrictive, whereas the proofs are significantly simpler compared to those reported in the literature. The results obtained extend and improve some previous results.     

Dynamical properties of families of discrete delay advection–reaction operators

A family of discrete delay advection–reaction operators is introduced along with an infinite matrix formulation in order to investigate the asymptotic behaviour of the orbits of their iterates. The infinite matrices obtained are triangular matrices with only one non-zero subdiagonal. We show that the elements of powers of these matrices can be written as distinctive products of two factors, one of them involving derivatives of the Lagrange polynomials of basic functions with the diagonal elements as nodes. The other factor consists of products of the subdiagonal elements. Consequently the convergence of the iterates of the operators depends on their eigenvalues and the products of their subdiagonal elements.     

Asymptotic analysis for an extended discrete Lotka–Volterra system related to matrix eigenvalues

The integrable discrete hungry Lotka–Volterra (dhLV) system is easily transformed to the qd-type dhLV system, which resembles the recursion formula of the qd algorithm for computing matrix eigenvalues. Some of the qd-type dhLV variables play a role for assisting the time evolution of the others. This property does not appear in the original dhLV system. In this article, we first show the existence of a centre manifold for the qd-type dhLV system. With the help of the centre manifold theory, we next investigate the local convergence of the qd-type dhLV system, and then clarify the monotonicity related to the qd-type dhLV variables at the final phase of the convergence.     

Stroboscopic averaging of highly oscillatory nonlinear wave equations

In this paper, we are concerned with stroboscopic averaging for highly oscillatory evolution equations posed in a Banach space. Using Taylor expansion, we construct a non‐oscillatory high‐order system whose solution remains exponentially close to the exact one over a long time. We then apply this result to the nonlinear wave equation in one dimension. We present the stroboscopic averaging method, which is a numerical method introduced by Chartier, Murua and Sanz‐Serna, and apply it to our problem. Finally, we conclude by presenting the qualitative and quantitative efficiency of this numerical method for some nonlinear wave problem. Copyright © 2014 John Wiley & Sons, Ltd.     

一类二阶Emden-Fowler型中立型时滞微分方程的区间振动性

对一类二阶Emden-Fowler型中立型时滞积分方程(a(t)x′(t))′+q<,1>(t)|y(t-σ<,1>)|<'α>sgn x(t-σ<,1>)+g<,2>(t)|y(t-σ<,2>)|<'β>sgn y(t-σ<,2>)=0,利用Riccati技巧和积分平均法,给出了一些判定其解振动的充分判据.这些判据仅...     

二阶延迟微分方程θ-方法的TH-稳定性

This paper is concerned with the TH-stability of second order delay differential equation. A sufficient condition such that the system is asymptotically stable is derived. Furthermore, a sufficient condition is obtained for the hnear θ-method to be TH-stable. Finally, the plot of stability region for the particular case is presented.     

基于时滞惯性流形的非线性Galerkin算法

针对Marion-Temam型非线性Galerkin方法可行性强烈依赖于最小解题规模的不足,利用时滞惯性流形的新思想,以二维Navier-Stokes方程为例,给出了该类非线性Galerkin方法的一种改进形式,并证明了改进后的方法在保持原方法优越性的同时,其可行性条件得到了很大的改善,从而,给出的是一种可行的高效稳定算法。     

Asymptotic behaviour of nonlinear difference equations

In this paper, we investigate the growth/decay rate of solutions of a class of nonlinear Volterra difference equations. Our results can be applied for the case when the characteristic equation of an associated linear difference equation has complex dominant eigenvalue with higher than one multiplicity. Illustrative examples are given for describing the asymptotic behaviour of solutions in a class of linear difference equations and in several discrete nonlinear population models.     

ASYMPTOTIC BEHAVIOR IN NONLINEAR DISCRETE-TIME NEURAL NETWORKS WITH DELAYED FEEDBACK

This paper is concerned with a delay difference system. Some interesting results are obtained for the asymptotic behaviors of the system. Our theorems improve the corresponding theorems in the relevant literature by removing the restriction of the initial conditions.     

关于Triebel空间上的算子值傅里叶乘子

利用Str6mberg-Torchinsky分解,给出了Triebel空间FEp.q(Rn,X)上算子值傅里叶乘子的一个充分条件.在rl相似文献   

数值求解延时微分方程的步长准则

１．引言 用一个数值方法求解下列延时微分方程：其中, ｆ： Ｒ × Ｃｄ × Ｃｄ → Ｃｄ为给定函数, Ｕ（ｔ）当上＞ ０时为未知函数,τ＞ ０为常数延时量,ф（ｔ）∈Ｃｄ为已知向量值函数．为了检验一个数值方法的数值稳定性,常用如下试验方程：来观察方法的数值稳定性,这里ａ,ｂ∈Ｃ（Ｃ为复数集）为已知常数,ф（ｔ）为给定的连续函数（ｔ≤０）． 定义 １［2］．延时微分方程（简记为ＤＤＥＳ）（３）被称为是渐近稳定的,如果（３）的每一个解Ｕ（ｔ）满足 方程(３)的特征方程为： 定义 ２［２］．一数值方法求解ＤＤＥＳ称为…     

一类二阶非线性摄动微分方程的振动性与渐近性

研究了一类二阶非线性摄动微分方程解的振动性质和渐近性质,建立了两个新的振动性与渐近性定理,推广和改进了已有的一些结果.