二阶中立型差分方程的振动性

研究了一类变系数的二阶中立型时滞差分方程的振动性,得到了该类方程振动及解的一阶差分振动的充分条件。     

二阶非线性中立型时滞差分方程的振动性

研究了一类具有多个变滞量的变系数的二阶非线性中立型时滞差分方程的振动性,得到了该类方程振动及其解的一阶差分振动的充分条件,推广了现有文献中的某些结果.     

一类二阶中立型差分方程的振动性

研究一类具有多个变滞量的变系数的二阶非线性中立型时滞差分方程的振动性．得到该类方程振动的充分条件及其解的一阶差分振动的充分条件,推广了现有文献中的相关结果．     

二阶半线性中立型差分方程的振动性准则

考虑二阶半线性中立型差分方程给出了方程(1)的解的振动性的充分条件．所有结果推广和改进了关于中立和时滞差分方程已有结果．     

具有变系数的二阶中立型差分方程的有界振动

研究一类具有连续变量的二阶中立型时滞差分方程，给出了该类方程一切有界解振动的几个充分条件.     

具连续变量的变系数偶数阶差分方程的有界振动

研究时滞差分方程解的性质在理论和应用中是非常重要的.本文借助研究离散变量的差分方程振动性的一般方法,研究了一类具有连续变量的变系数偶数阶中立型差分方程的有界解的振动性,给出了有界解振动的几个充分条件.     

具有变系数的二阶中立型差分方程

研究一类具有变系数的二阶中立型时滞差分方程 △τ^2[x（t）-c（t）x（t-τ）]=p（t）x（t-σ），t≥t0〉0 的解的振动性，给出了该类方程一切有界解振动的几个充分条件．     

一类二阶非线性中立型差分方程的振动性

研究了二阶非线性中立型差分方程Δ2(xn+pxn-l)+qnf(xn-k)=0的振动性,获得了该类方程振动的三个充分性定理.所得结果将一阶非线性中立型差分方程已有振动性的相应结论推广到了二阶非线性中立型差分方程.     

一类二阶中立型时滞差分方程解的振动性

研究了二阶中立型时滞差分方程Δ(an(Δ(xn+pnxn-τ))α)+qnxnβ-σ=0解的振动性的几个充分条件,改进和推广了文献中的有关结论。     

具有连续变量的二阶中立型时滞差分方程的振动性

研究了一类具有连续变量的二阶中立型时滞差分方程△(2Υ)(x(t) -px(t- γ) =mΣi=1 qi(t)x(t-σi),t ≥ t0 ＞ 0的振动性,给出了其有界解振动的几个充分条件.     

OSCILLATION THEOREMS FOR SECOND ORDER NEUTRAL DIFFERENCE EQUATIONS

The aim of this paper is to study the oscillation of second order neutral difference equations.Our results are based on the new comparison theorems,that reduce the problem of the oscillation of the second order equation to that of the first order equation.The comparison principles obtained essentially simplify the examination of the equations.     

一类二阶非线性差分方程的振动性定理

应用分析方法,研究了一类二阶非线性差分方程解的振动性质,获得了一个新的振动性定理,推广和改进了已知的一些结果.     

一类具有非线性中立型的非线性变时滞差分方程的振动性

考虑具有非线性中立项的二阶非线性变时滞差分方程,获得了该方程及其差分算子振动的充分条件.     

COMPARISON AND OSCILLATION THEOREMS FOR AN ADVANCED TYPE DIFFERENCE EQUATION

ＣＯＭＰＡＲＩＳＯＮ　ＡＮＤ　ＯＳＣＩＬＬＡＴＩＯＮ　ＴＨＥＯＲＥＭＳ　ＦＯＲ　ＡＮ　ＡＤＶＡＮＣＥＤ　ＴＹＰＥ　ＤＩＦＦＥＲＥＮＣＥ　ＥＱＵＡＴＩＯＮＣＯＭＰＡＲＩＳＯＮＡＮＤＯＳＣＩＬＬＡＴＩＯＮＴＨＥＯＲＥＭＳＦＯＲＡＮＡＤＶＡＮＣＥＤＴＹＰＥ...     

OSCILLATION CRITERIA FOR SECOND-ORDER NONLINEAR DIFFERENCE EQUATIONS WITH CONTINUOUS VARIABLE

Some new oscillation criteria are given for a second order nonlinear difference equation with continuous variable. Our results generalize and improve the recent criteria of Zhang Z.G., Bi P. and Chen J.F..     

Oscillation criteria for a forced mixed type Emden-Fowler equation with impulses

Some oscillation criteria for a forced mixed type Emden-Fowler equation with impulses are given. When the impulses are dropped, our results extend those of Sun and Meng [Y.G. Sun, F.W. Meng, Interval criteria for oscillation of second-order differential equations with mixed nonlinearities, Appl. Math. Comput. 15 (2008) 375-381], Sun and Wong [Y.G. Sun, J.S.W. Wong, Oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities, J. Math. Anal. Appl. 334 (2007) 549-560] for second-order forced ordinary differential equation with mixed nonlinearities, Nasr [A.H. Nasr, Sufficient conditions for the oscillation of forced superlinear second order differential equations with oscillatory potential, Proc. Am. Math. Soc. 126 (1998) 123-125], Yang [Q. Yang, Interval oscillation criteria for a forced second order nonlinear ordinary differential equations with oscillatory potential, Appl. Math. Comput. 135 (2003) 49-64] for forced superlinear Emden-Fowler equation, Kong [Q. Kong, Interval criteria for oscillation of second-order linear differential equations, J. Math. Anal. Appl. 229 (1999) 483-492] for unforced second order linear differential equations, and Wong [J.S.W. Wong, Oscillation criteria for a forced second order linear differential equation, J. Math. Anal. Appl. 231 (1999) 235-240] for forced second order linear differential equation.     

OSCILLATION AND ASYMPTOTIC BEHMIOR OF SECOND ORDER NONLINEAR NEUTRAL DIFFERENCE EQUATION

1IntroductionLetR=(--co,co),R =[0,co)andN={l,2,'.},considerthesecondordernonlillearneutraldifferenceequationThesubjectissupportedbyHeilongjiangProvinceNaturalScienceF(,undatfonN,l,,hi6N,andletk~ma-c{li,hifiEIm,jeI.}.ThefunctionfiisrealvaluedcontinuousonR…