1) infinite-point boundary value problems
无穷多点边值问题
1.
This paper is concerned with the infinite-point boundary value problems of second order ordinary differential equation(ODE) and some theorems related to the existence of nontrivial solutions of this problem is obtained.
本文运用锥上的不动点定理,建立二阶常微分方程无穷多点边值问题非平凡解的存在性定理。
2) infinite-many point boundary value problem
无穷点边值问题
1.
The method of lower and upper solutions is established for the infinite-many point boundary value problem of the first-order ordinary differential equation{x′(t)=f(t,x(t)),a.
建立一阶常微分方程无穷点边值问题{x′(t)=f(t,x(t)),a。
3) infinite boundary value problem
无穷边值问题
1.
Positive unbounded solutions of infinite boundary value problem for second-order singular differential equation
二阶奇异微分方程无穷边值问题的正无界解
2.
In this paper,by constructing a special cone and using fixed point theorem on cone,the existence of at least one positive unbounded solutions of infinite boundary value problem of a class of singular differential equations is obtained.
通过构造一个特殊的锥,利用锥上的不动点定理讨论了一类二阶奇异微分方程无穷边值问题正无界解的存在性。
3.
In this article, we study the infinite boundary value problems for first order nonlinear impulsive differential equations with ″supremum″ by means of the upper and lower solution method and the monotone iterative technique, and obtain the existence theorems for their extremal solutions.
应用上下解方法和单调迭代技术研究了带有上确界的一阶非线性脉冲微分方程无穷边值问题,并获得了其极值解的存在性结果。
4) multi-point boundary value problem
多点边值问题
1.
Solutions of (n-1,1) type multi-point boundary value problems for higher-order differential equations;
高阶微分方程(n-1,1)型多点边值问题的解
2.
Solvability of a second order multi-point boundary value problem with generalized Sturm-Liouville boundary condition;
一类二阶广义Sturm-Liouville边界条件多点边值问题的可解性
5) multi-point boundary value problems
多点边值问题
1.
On existence solutions for multi-point boundary value problems at resonance;
关于具共振条件多点边值问题解的存在性
2.
Existence solutions for multi-point boundary value problems with two dimension kernel at resonance;
具二维核共振条件多点边值问题解的存在性
3.
By applying a new fixed point theorem,it was obtained that the existence of at least three positive solutions to the second order nonlinear multi-point boundary value problems as follow: u′ ′(t) + f(t,u(t)) = 0,t∈ [0,T ],u′(0) = 2 1()m i i ibu ξ? =∑′,21 1()ki(i) m i(i) i i ku T a u ξ? a u ξ = = += ∑? ∑.
利用一个新的不动点定理讨论了一类二阶非线性多点边值问题:u′′(t)+f(t,u(t))=0,t∈[0,T]。
6) multipoint boundary value problem
多点边值问题
1.
Existence and iteration of monotone positive solutions to a class of p-Laplacian multipoint boundary value problem
一类p-Laplacian多点边值问题单调迭代正解的存在性
2.
We consider the multipoint boundary value problem for the one-dimensional p-Laplacian {(φp(u′))′(t)+q(t)f(t,u(t),u′(t))=0,0
利用Avery-Peterson不动点定理,在射线上讨论了如下p-Laplacian算子方程多点边值问题,{(φp(u′))′(t)+q(t)f(t,u(t),u′(t))=0,0
补充资料：微分边值问题的差分边值问题逼近
微分边值问题的差分边值问题逼近
approximation of adifferentia) boundary value problem by difference boundary value problems
微分边值问题的差分边值问题通近{即proxlm浦训ofa山fferential肠扣nd即卿阁此pn由lemby山ffe悦n沈b侧n-da仔耐ue pn由lems;all即旧K。肠，au舰皿呻加脚.胆，日峨成峥ae侧甫，阴，加琳3“心犯川角! 关于未知函数在网格_[的值的有限(通常是代数的)方程组对微分方程及其边界条件的一种逼近.通过使差分间题的参数(网格步长)趋于零，这种逼近会越来越准确. 考虑微分边值问题L:、二0，lu!l二O的解“的川算，其中L“=0是微分方程Iu!二0是一组边界条件.u属于定义在边界为r的给定区域从上的函数所组成的线性赋范空间U设D、。是网格(llL微分算子的差分算子通近(approx，matlon of a ditTere;ltl;，1 op-erator by differe们优。详rators))，并设U*是rlJ定义价该网格上的函数。*所组成的线性赋范空间.设卜j、厂函数v在几;的点上的值表卜在打。中引进范数使得对任意的函数，;〔创，以手‘等式成盆: 恕伽训、·三{训‘现在用近似计算“在D*。中的点上的值表luJ的问题一/*{司、=0代替求解“的问题.这里了*【川。是一组关一)网格函数。*任U。的值的(作微分)方程 设。*是U、中的任意函数.令二。。、二叭片设小是线性赋范空间，对任意的叭6u*有势*。中，二称才*“*二0是对微分边值问题L“二0，l川，一0石其解空间_L的P阶有限差分逼近，若 {}了*lu奴{}。*二O(h尸)方程组J、“*=0的实际构造涉及分别构造它的两个子方程组IJ*u*=o和l、u*}。二0.对L*u儿=0，使用微分方程的差分方程通近(approximat，on。》f a dll化r‘:ntia}equation by differer，沈equations).附加方程I。，、、}:=(”利用边界条件l川。=0来构造. 对无论怎样选取的U、与中人的范数，上面所描述的逼近都无法保证差分问题的解u、收敛到准确解“(见{2])，即等式 {，砚}1 lul*一“六{}、;。成立. 保证收敛性的附加条件是稳定性(见{3!，{5!18])，有限差分间题必须具有这一性质.称有限差分间题了r八“、=0是稳定的，若存在正数占>oh。>0使得对任意毋*‘。*，}一甲*{}<。，h<权，方程一气:二甲*有唯一解:*已认，且此解满足不等式 1}:儿一u*}}:。“{}。、}{。，其中C是与h或右端扰动叭无关的常数，“、是无扰动问题一/*。=O的解‘如果褂于问题的解u存在同时差分问题气“、二O关于解“以p阶精度逼近微分问题，而且是稳定的，则差分问题具有同样阶的收敛性，即 }1[uL一吟}l叭=O(hp). 例如，问题 ，，、_au au L(“)三.举一拼=0，I>0.一的
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