1) perturbed Volterra-type difference equations
扰动Volterra型差分方程
1.
Stability in terms of two measures for perturbed Volterra-type difference equations;
关于扰动Volterra型差分方程的两度量稳定性(英文)
2) Volterra difference equation
Volterra差分方程
1.
First, consider the boundedness and asymptotic equivalence of the solutions of the Volterra difference equationand corresponding the perturbation systemFixed point theorem is used to investigate the existence of the solution of the perturbed system.
本文主要分两部分,首先讨论了Volterra差分方程和相应的扰动系统解的有界性和渐进等价性,并且运用压缩映射求不动点的方法证明扰动系统解的存在性。
3) Volterra type integro-differential-difference equation
Volterra型积分微分差分方程
1.
Singularly perturbed nonlinear boundary problem of second order Volterra type integro-differential-difference equation;
二阶Volterra型积分微分差分方程的非线性边值问题的奇摄动
2.
The existence and uniqueness and asymptotic estimates of solution for nonlinear boundary value problem of Volterra type integro-differential-difference equation is studied by means of differential inequality theories.
利用微分不等式理论研究了二阶Volterra型积分微分差分方程非线性边值问题的解的存在性。
4) Volterra type integral equation
Volterra型积分方程
1.
In this paper,the concept of condition contraction operator is defined,the existence of fixed points of this class of operators and the existence as well as the uniqueness of solutions for nonlinear Volterra type integral equations in Banach spaces are discussed.
给出了Banach空间条件压缩算子定义,讨论了此类算子不动点的存在性和Banach空间中非线性Volterra型积分方程解的存在性和唯一性。
5) Volterra integral equation
Volterra型积分方程
1.
The Unique Solution of Nonlinear Impulsive Volterra Integral Equation in Banach Space;
Banach空间中非线性脉冲Volterra型积分方程的唯一解
2.
The relationship between the approximate and exact solutions of a class of nonlinear Volterra integral equations is considered.
首先在Banach空间中考虑一类非线性Volterra型积分方程的逼近解与精确解之间的关系,由此并通过比较定理在紧型条件下获得方程解的存在性结果。
6) Volterra type integral equations
Volterra型积分方程
1.
Several fixed point theorems and applications for Volterra type integral equations;
几个不动点定理及其在Volterra型积分方程中的应用
2.
In this paper, an existence theorem on the coupled minimal and maximal positive solutions for a class of discontinuous nonlinear Volterra type integral equations involving linear Fredholm type integral in ordered Banach spaces is obtained.
在Banach空间中得到了一类含有线性Fredholm型积分的不连续非线性Volterra型积分方程的耦合正解 。
3.
In this paper,an existence theorem on the coupled minimal and maximal positive solutions for a class of discontinuous nonmonotone Volterra type integral equations in Banach spaces is obtained.
在Banach空间中得到了一类不连续非增Volterra型积分方程的最大最小耦合正解 ,并给出了不连续非增Volterra型积分方程初值问题的应用 。
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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参考词条