1) first difference equation
一阶差分方程
2) First-order partial difference equation
一阶偏差分方程
3) first order autonomous difference equations
一阶自治差分方程
1.
For the first order autonomous difference equations under the assumption of continuity of the right- hand function f ( x ) ,this paper established the stability criteria for the equilibrium points just in terms of the Dinileft- hand and right- hand derivatives.
在一阶自治差分方程右端函数 f ( x)仅为连续的情况下 ,只须根据 Dini左、右导数 ,即给出了其平衡点稳定性的判据 ,减弱了已知结果对 f( x)具有各阶连续导数的要求 ,并用例子说明了所得结果之应
5) second order difference equation
二阶差分方程
1.
New oscillation criteria are presented in this paper for nonlinear second order difference equations:Δ2bun+∑mi=1ainfi(un,Δbun)=0, n=0,1,2,…
对非线性二阶差分方程Δ２ｂｕｎ＋∑ｍｉ＝１ａｉｎｆｉ（ｕｎ，Δｂｕｎ）＝０，ｎ＝０，１，２，…给出并证明了它的有界解振动的新充分判则。
2.
Oscillation criteria for nonlinear second order difference equations are established,Results obtained improve theorems in the literature[5].
本文建立了非线性二阶差分方程的若干振动准则，所得结果改进了文［５］中相应的定理。
6) higher order difference equation
高阶差分方程
1.
Employing critical point theorem,we study a higher order difference equation sum from i=0 to k a_i(x_(n-i)+x_(n+i))+f(x_(n+1),x_n,x_(n-1))=0,n∈Z,k∈N and obtain some sufficient conditions ensuring the existence of nontrivial M-periodic solution for such a equation.
本文应用临界点理论获得了一类高阶差分方程sum from i=0 to k a_i(x_(n-i)+x_(n+i))+f(x_(n+1),x_n,x_(n-1))=0,n∈Z,k∈N非平凡M-周期解存在的充分条件。
补充资料：二阶线性齐次微分方程
二阶线性微分方程的一般形式为
ay"+by'+cy=f(1)
其中系数abc及f是自变量x的函数或是常数。函数f称为函数的自由项。若f≡0，则方程（1）变为
ay"+by'+cy=0（2）
称为二阶线性齐次微分方程，而方程（1）称为二阶线性非齐次微分方程。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条