1) neutral differential difference equation
中立型微分差分方程
1.
by means of variational structure and critical P Oint theory, we give some criteria for the existence of periodic solutions to a Class of second-order neutral differential difference equations as the followin G type(t-τ)-x(t-τ)+f(t,x(t),x(t-τ),x(t-2τ))=0With the boundary value conditionX(0)=x(2kτ), (0)=(2kτ)Where k is a given positive integer and τ is a positive number.
考虑如下二阶中立型微分差分方程的边值问题 :x(t-τ) - x(t-τ) + f (t,x(t) ,x(t-τ) ,x(t- 2τ) ) =0x(0 ) =x(2 kτ) ,x(0 ) =x(2 kτ)其中 k是任意给定的正整数 ,τ为正实数 。
2.
Oscillation of the first order nonhomogeneous neutral differential difference equationsis discussed .
讨论非齐次中立型微分差分方程d/dt[x(t)+Cx(t-τ)]+P(ι)x(t-σ)+f(ι)=0 t≥t_0的振动性,获得某些充分条件,并推广了某些齐次方程的结果。
2) neutral type difference differential equation
中立型微分-差分方程
3) neutral difference equation
中立型差分方程
1.
Oscillation of forced neutral difference equations with positive and negative coefficients;
具有强迫项正负系数中立型差分方程的振动性
2.
Oscillation of neutral difference equations with "maxima";
带有极大值项的中立型差分方程的振动性
3.
Oscillation for a class of even order neutral difference equations with continuous arguments;
具连续变量的偶数阶中立型差分方程的振动性
4) neutral difference equations
中立型差分方程
1.
Asymptotic behavior of solutions to forced neutral difference equations;
具有强迫项的中立型差分方程解的渐近性
2.
Some sufficient conditions for oscillation of the nonlinear neutral difference equations;
非线性中立型差分方程振动的充分条件
3.
Oscillation for a class of nonlinear neutral difference equations with variable delay was studied in this paper.
考虑一类具有可变时滞的非线性非自治中立型差分方程 ,得到了这类方程的振动准则及这类方程存在最终正解的充分条件 。
5) neutral delay difference equation
中立型差分方程
1.
Asymptotic stability of neutral delay difference equations with perturbing;
具有扰动的中立型差分方程的渐近稳定性
2.
Bounded Oscillation for second order neutral delay difference equation Δ2(Xn-PnXn-σ)= was discussed,where n∈N+,0≤Pn<1,0<N≤Qn≤M;σ,τi are positive integer;αi is the quotient of two positive odds,and αi=1.
讨论二阶不稳定型中立型差分方程Δ2(Xn-PnXn-σ)=(n∈N+,0≤Pn<1,0
3.
Consider the second order neutral delay difference equationΔ2(xn+cxn-τ)+pnf(xn-σ)=0,n∈N(n0),the existence of a nonoscillatory solution is obtained by Krasnoselskii′s fixed point theorem.
讨论二阶中立型差分方程Δ2(xn+cxn-τ)+pnf(xn-σ)=0,n∈N(n0)。
6) neutral differential equation
中立型微分方程
1.
Oscillatory criteria of second order neutral differential equations;
二阶中立型微分方程的振动准则(英文)
2.
A class of second order nonlinear neutral differential equations is considered.
研究一类二阶非线性中立型微分方程,通过引入参数函数,结合完全平方技术,给出了该类方程解振动的判别准则,所得结果推广了已有文献的部分结果。
3.
In this paper,we consider certain second order nonlinear neutral differential equation.
研究了一类二阶非线性中立型微分方程的振动性,建立了此类方程的所有解振动的充分条件。
补充资料:微分方程的差分方程逼近
微分方程的差分方程逼近
approximation of a differential equation by difference equations
微分方程的差分方程通近【app拟。mati.ofa山价犯n-ti习闪姗柱.by山血魂.理equa西姗;即即肠。砚田朋.朋巾卜碑四.别吸.。印冲.旧e朋,pa3I.ecTll目M] 微分方程用关于未知函数在某种网格上的值的代数方程组的逼近,当网格的参数(网络、步长)趋于零时可使得逼近更加精确. 设L(Lu可)是某个微分算子,几(L声。=几,。。任叭,人“凡)是某个有限差分算子(见徽分算子的差分算子通近(aPProximation of a dilferential operator by dif-feren沈。perators”.如果算子L、关于解u逼近算子L,其阶为p,即如果 }}Lh[u]*I}汽=o(hp),那么有限差分式L声、二0(o任凡)称为关于解“对微分方程Lu=O的P阶逼近. 构造有限差分方程L声*=0关于解u逼近微分方程Lu=0的最简单例子是将Lu的表达式中每个导数用相应的有限差分来代替. 例如,方程 _子“.,、血._,_八_一n Lu三书舟+P(x)于+q(x)u=U ~“一dxZr‘~产dxl‘’可用有限差分方程 L‘“‘三生理二丛吐丛二+ h‘ U~丰I一U,_I_ +尸(x们厂竺二兹巴几十,(x功)u朋一o作二阶精度逼近,其中网格几。和几;由点x.“。h组成(m是一整数),“.是函数u*在点x.的值.又,方程 au aZu L“三共牛一斗冬二0, --一ar ax,可用关于光滑解的两种不同的差分近似来逼近: _.月+1_”月气.月上.” 一门、“nt4用“用十l‘“阴l“用一I八 于九‘(撇式格式(exPlie,}seheme))和! “几’l一嗽试,‘l}一翔二,曰衅,‘从 拭’价二一一-一—一了一--一一几,(隐式格式(一mf)liczt scheme)),其中网格D*。和D*:由点(x。,甲=(川入,似)组成,:二rhZ,r二常数,巾和n是整数,。二是函数翻、在网格点(x,,t。)的值.存在这样的有限差分算子L,它对微分算子L的逼近,仅关于方程L。一0的解。特别好,而关于其他函数则差一些.例如,算一子L*L*U。三兴,·卜·夸卫一尹{刁内队引〔其中汀二·。州一随甲‘气))关f任意的光滑函数。(*)是算 广L- d仪 L“一…一甲〔戈,“)Z(工) 办的一阶逼近(_关于八)、而关于方程大u=O的解却是二阶逼近(假定函数:,充分光滑)在利用有限差分方程与。。
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