二阶非线性中立型时滞微分方程的振动准则

文章考虑二阶非线性中立型微分方程a(t)x(t)+∑li=1ci(t)x(t-τi(t))″+∑mi=1pi(t)fi(x(t-δi(t)))-∑ni=1qi(t)gi(x(t-σi(t)))=0的振动性,获得了该方程所有解振动的充分条件,推广了有关文献的结果.     

Notes on Oscillation of Solution for aCertain Second Order Neutral Equation

Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｃｏｎｓｉｄｅｒｏｓｃｉｌｌａｔｏｒｙｏｆｅｑｕａｔｉｏｎ（１）［ｘ（ｔ）＋ｃｘ（ｔ－τ）］″＋∫ｂａｐ（ｔ，ξ）ｘ［ｇ（ｔ，ξ）］ｄσ（ξ）＝０，（１）ｗｈｅｒｅτ０；ｐ（ｔ，ξ），ｇ（ｔ，ξ）∈Ｃ（［ｔ０，＋∞）×［ａ，ｂ］，Ｒ）；ｇ（ｔ，ξ）ｔ，ξ∈［ａ，ｂ］；ｇ（ｔ，ξ）ａｒｅｎｏｎ－ｄｅｃｒｅａｓｉｎｇｗｉｔｈｔｏｔ，ξ，ｒｅｓｐｅｃｔｉｖｅｌｙａｎｄｌｉｍｔ→＋∞ｍｉｎξ∈［ａ，ｂ］｛ｇ（ｔ，ξ）｝＝＋∞，σ（ξ）∈（［ａ，ｂ］，Ｒ）ｉｓｎｏｎｄｅｃｒ…     

具连续变量的二阶中立型差分方程的振动性

研究一类具有连续变量的二阶中立型时滞差分方程△r^2[x（t）-cx（t-τ）=p（t）x（t-σ）的解的振动性，给出了其有界振动的几个充分条件．     

具有正负系数的二阶脉冲中立型方程的振动性

考虑一类具有正负系数的多时滞二阶线性脉冲中立型微分方程,证明了该方程解的振动性等价于一类非脉冲中立型方程解的振动性,得到了方程所有解存在的充分条件.     

具有时滞的利率-流通量方程的建立及其应用

本文对金融网络建立了带有时滞的利率-流通量方程，应用时滞微分方程理论，我们得到金融网络中，各节点利率最终将稳定于其基本利率的充分必要条件；给出了各节点利率均振动的充分必要条件以及存在周期解的充分必要条件。     

一类Lyness方程的一些性质

本文主要研究下列Lyness方程的性质Xn+1=Xn\(a+b0Xn+b1Xn-1+…+bkXn-k)Xn-k-1,n=0,1,2,…,其中a,b0,b,…,bk∈[0,∞),a+k∑i=0bi＞0,k∈{0,1,2,…}.文中给出了方程(*)严格振动的充分条件,以及环长和环上极值的位置.另外,还得到了方程(*)在特殊情况下分别具有4,5,6周期的必要充分条件.本文的结果改进并推广了一些已知结果.     

Oscillatory and Asymptotic Behavior of Solutions for Nonlinear Impulsive Delay Differential Equations

The oscillatory and asymptotic behavior of the solutions for third order nonlinear impulsive delay differential equations are investigated. Some novel criteria for all solutions to be oscillatory or be asymptotic are established, Three illustrative examples are proposed to demonstrate the effectiveness of the conditions.     

A ring-cavity for a quadrupled Nd-Yag lasera

Summary A new high-powered ultraviolet laser system is proposed. The system doubles the infrared light from a Nd-Yag laser mode-locked at 100 MHz, injects this light into a storage-ring cavity to accumulate a high power in the visible and then doubles this into the ultraviolet at 2600 ?. The power levels anticipated at this wavelength are much larger than those of commercially available c.w. lasers. The new system can have a far-reaching impact in basic research and, even more so, in a great many industrial applications.     

高维离散动力系统的平稳振荡

本文应用不动点原理研究了高维离散周期系统的存在周期解的唯一性和稳定性,给出了存在平稳振荡和唯一周期解的充分条件.     

Tauberian theorems for Abel limitability method

This paper addresses conditions for the Abel method of limitability to imply convergence and subsequential convergence.