1) n-point boundary value problems
n-点边值问题
1.
Based on new fixed point theorem,a sufficient condition of at least triple positive solutions for second order nonlinear n-point boundary value problems is obtained.
利用一个新的不动点定理,得到了二阶非线性n-点边值问题:u″(t)+f(t,u(t))=0,t∈(0,1)u′(0)=∑n-2i=1biu′(ξi),u(1)=∑ki=1aiu(ξi)-∑n-2i=k+1aiu(ξi)至少存在三个正解的一个充分条件,其中0<ξ1<ξ2<…<ξn-2<1,ai,bi∈[0,∞)且满足0<∑ki=1ai-∑n-2i=k+1ai<1,∑n-2i=1bi<1。
2) n-point boundary value problem
n点边值问题
1.
Research differential inequalities and existence of solution of nonlinear n-point boundary value problem of second order differential equations as followingy″=f(t,y,y′),a<t<b,h[y(a),y′(a),y(t1),y(t2),…,y(tn-2)]=0,g[y(t1),y(t2),…,y(tn-2),y(b),y′(b)]=0.
研究二阶微分方程的非线性n点边值问题y″=f(t,y,y′),a
2.
And then the suitable functionals are constructed to prove the existence of three positive solutions for second-order n-point boundary value problem in Banach spaces by using the fixed point theorem proved above.
利用严格集压缩映象的不动点定理讨论紧型条件下的Banach空间n点边值问题。
3) two-point boundary value problem
两点边值问题
1.
Existence and uniqueness of solutions for two-point boundary value problems of second order difference equation;
二阶差分方程两点边值问题的存在性与惟一性
2.
Solutions of two-point boundary value problems of integro-differential equations in Banach spaces;
Banach空间积-微分方程两点边值问题的解
3.
Solvability of p-Laplacian two-point boundary value problems with obstruction band;
障碍带条件下p-Laplace方程两点边值问题的可解性
4) three-point boundary value problem
三点边值问题
1.
Existence of multiple positive solutions for one kind of second-order three-point boundary value problem;
一类二阶三点边值问题多重正解的存在性
2.
Existence and multiplicity of positive solutions to nonlinear fourth-order three-point boundary value problems;
非线性四阶三点边值问题的正解存在性与多解性
3.
Solvability of a class of second-order three-point boundary value problems with first derivative;
一类含一阶导数的二阶三点边值问题的可解性
5) two-point boundary value problems
两点边值问题
1.
Existence of solutions for two-point boundary value problems of second order impulsive integrodifferential equations of mixed type;
二阶混合型脉冲微分—积分方程两点边值问题解的存在性
2.
Existence of multiple solutions for a kind of two-point boundary value problems of ordinary differential equations;
一类常微分方程两点边值问题的多解存在性
3.
For a class of two-point boundary value problems,by virtue of one-dimensional projection interpolation and finite element superconvergence fundamental estimations,it was proved that the nodal recovery derivative obtained by Yuan s element energy projection(EEP) method had the optimal order superconvergence on condition that the degree of finite element space is no more than 4.
利用一维投影型插值与有限元超收敛基本估计,对一类两点边值问题,严格证明了袁驷等人由单元能量投影(EEP)法获得的节点恢复导数,当有限元空间的次数不超过4时,具有最佳阶超收敛。
6) TPBVP
两点边值问题
1.
Numerical Solution of TPBVP in Optimal Lunar Soft Landing;
月球最优软着陆两点边值问题的数值解法
2.
This optimal form is considered as a Two-Point Boundary Value Problem (TPBVP), and the shooting method based on an initial variable guess set can be used to search the solution.
其次,依据庞特里雅金最小值原理推出了机器人本体两点间运动时间最优的控制律,并将该非线性方程组的求解看作是一个两点边值问题,通过引入简单打靶法以及一种初值猜测技术来求解该方程组。
3.
The loading time history reconstruction is transferred to a two-point boundary value problem(TPBVP) with performance index J,and then the problem with multi-input and multi-output is solved by Riccati matrix.
首先基于一个模态空间的正向模型,设计一个最优化状态跟踪器并构造出性能指标J,将载荷时程的重构转变成一个两点边值问题的求解。
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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