具有时滞的非线性强迫微分方程振动的充分必要条件

对于一类特殊的具有时滞的二阶次线性强迫微分方程x"(t) +a (t)|x(τ(t))|γsgnx(τ(t)) =g(t)(0＜τ＜1),给出了它的所有解振动的一个充要条件.     

On a semilinear Schrödinger equation with critical Sobolev exponent

We consider the semilinear Schrödinger equation , , where , are periodic in for , 0$">, is of subcritical growth and 0 is in a gap of the spectrum of . We show that under suitable hypotheses this equation has a solution . In particular, such a solution exists if and .

     

Oscillation and Nonoscillation of Higher Order Self-Adjoint Differential Equations

Oscillation and nonoscillation criteria for the higher order self-adjoint differential equation (-1)ⁿ(t^alphay⁽ⁿ⁾)⁽ⁿ⁾+q(t)y = 0 (*) are established. In these criteria, equation (*) is viewed as a perturbation of the conditionally oscillatory equation (-1)ⁿ(t^alphay⁽ⁿ⁾)⁽ⁿ⁾ - µ,t^2n-y = 0, where _n, is the critical constant in conditional oscillation. Some open problems in the theory of conditionally oscillatory, even order, self-adjoint equations are also discussed.     

Global Attractivity of the Equilibrium of a Nonlinear Difference Equation

The authors consider the nonlinear difference equation x_n+1=x_n+x_n-kf(x_n-k),n=0,1,(0.1) where (0,1), k 0,1, and f C¹[[0,), [0,)] with f(x) < 0.They give sufficient conditions for the unique positive equilibrium of (0.1) to be a global attractor of all positive solutions. The results here are somewhat easier to apply than those of other authors. An application to a model of blood cell production is given.     

FORCED OSCILLATION AND APPLICATION OF FUNCTIONAL DIFFERENTIAL INEQUALITIES

In this paper we study the oscillations for a class of functional differential inequalities. By using these properties some forced oscillations to the boundary value problems of functional partial differential equations are established.     

OSCILLATION FOR A CLASS OF LOGISTIC EQUATIONS

The oscillation of a delay difference equationis studied and the necessary and sufficient condition for all positive solutions of (E) to oscillate about its positive equilibrium is obtained.     

NECESSARY AND SUFFICIENT CONDITION FOR OSCILLATION OF A CLASS OF HIGHERORDER NEUTRAL EQUATIONS

ＮＥＣＥＳＳＡＲＹＡＮＤＳＵＦＦＩＣＩＥＮＴＣＯＮＤＩＴＩＯＮＦＯＲＯＳＣＩＬＬＡＴＩＯＮＯＦＡＣＬＡＳＳＯＦＨＩＧＨＥＲＯＲＤＥＲＮＥＵＴＲＡＬＥＱＵＡＴＩＯＮＳＬｉｎＹｉｚｈｏｎｇ（林宜中）（ＦｕｊｉａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，福建师范...     

具有连续变量的差分方程的振动性

本文建立了具有连续交量差分方程的振动性判据，其结果改进了文献中的某些已知结果．     

CHARACTERISTIC EXPONENTS FOR SECONDORDER PERIODIC LINEAR DIFFERENTIAL EQUATION

1IntroductionandMainResultsItiswellknownthatwhenp'--4q>0,secondorderautonomoussystemhastwocharacteristicexponentsfsothefollowingpropositionsareobvious.Proposition1Assumeq<0,then(1.1)hastwocharacteristicexponentswithoppositesigns.Proposition2Assumeq>0andp'…     

阻尼Bloch振荡和负微分电导现象的简单理论分析

用能带理论分析一维超晶格电子在直流外场作用下的阻尼运动，对Ｂｌｏｃｈ振荡和负微分电导现象给出清楚的物理图象，并通过数值解得到有阻尼时振荡频率随外场增加而趋近于Ｂｌｏｃｈ频率的一般规律。