Any iterative sequence generated by the algorithms is a upper solution or a lower solution sequence,which converges monotonically to the solution of the problem.
所得的迭代序列为上解序列和下解序列,它们均单调收敛于问题的准确解,本文建立了这些算法的比较定理。
If there exist α and β respestively as upper and lower solutions ,we obtain sufficient conditions in to guarantee the existence of a solution between the lower soeution β and the upper solution α by making two monotoe sequences{α_n},{β_n},non-increasing and non-decreasing.
对六阶边值问题u(6)(x)= (x,u(x),u"(x),u(4)(x)),0
In this paper, the same theory is obtained by constructing new upper solution function, without the semi-Lipschitz condition.
通过改进Bainov等关于脉冲微分系统周期边值问题比较原理的证明方法,构造新的上解,在不需要脉冲I_k(x)关于x的半Lipschitz条件的情况下,得到了同样的比较原
On the Supersolution and Subsolution of Discrete HJB Equation;
关于离散HJB方程的下解与上解
In this paper,we extend case some their conclusions to systems and prove the existence for supersolution and subsolution in systems.
首先给出了完全非线性单调二阶椭圆方程组Neumann问题上解和下解的定义,然后证明了这类方程组Neumann问题上解和下解的存在性。
By applying the"supersolution- subsolution"method,a simple descriminat is obtained for the existence of positive entiresolutions.
本文讨论一类半线性椭圆方程，应用“上解－下解”的方法，得到正整解存在性的一个简单的判别式。
In this thesis, we study a class of higher quasi-linear elliptic hemi-variational inequalities, define its subsolution,supersolution and extremal solution and generalize the sub-supersolution method to this class of quasi-linear elliptic hemi-variational inequalities.
本文讨论了一类高阶拟线性椭圆半变分不等式，定义了其上解、下解及端解，将上下解方法推广到了此类高阶拟线性椭圆半变分不等式，并利用上下解方法证明了其解及端解的存在性以及上下解之间的解集的紧性。
In this paper,extremal solutions for the(PBVP) are obtained when the lower solution is greater than of equals to the upper solution by means of the monotone technique.
本文利用单调叠代技巧证明了当下解≥上解时，（ＰＢＶＰ）解的存在性。
The problem has solutions if and only if there exists a lower solution x and an uppersolution y and x(t)≤y(t) for all 0≤t≤1.
此问题有解当且仅当有一个上解y和一个下解x，且对所有的0≤t≤1，都有x（t）≤y（t）。
In this paper, the necessary and sufficient conditions of the lower solution and uppersolution are obtained for both the second order impulsive differential systems with periodicboundary value and the first order ones.
文中建立了二阶周期边值脉冲微分系统的上解、下解与一阶周期边值脉冲微分系统的上解、下解的充分必要关系，进一步在维数ｎ≥２时，解决了二阶脉冲微分系统周期边值问题的比较结果。
The limitation theorem of g-supersolution for BSDEs under non-Lipschitzian coefficient;
非Lipschitz条件下的倒向随机微分方程的g-上解的极限定理
For Backward Stochastic Differential Equation with jumps and an increasing predictable RCLL process as its penalization term,we have defined g-supersolution for such a BSDE and obtained the limit theorem.
对带跳和一个右连左极的增过程作为惩罚项的倒向随机微分方程定义g-上解,并得到极限定理,作为其应用,在变量(y,z,q)受限条件下,讨论该方程的最小g-上解存在唯一性。
In order to get the result the author investegates the existence and uniqueness of solution for a class BSDEs with the same driftcoefficient g, the comparison theorem, and lastly the limitation theorem of g-supersolution.
为此讨论一类漂移系数g( s,· ,· )关于 ( y,z)不满足 Lipschitz条件的倒向随机微分方程解的存在唯一性 ,运用 Biharis不等式证明了一类倒向随机微分方程的比较定理以及 g-上解的极限定理 。
Define and consider very weak solutions,very weak supersolutions and very weak subsolutions for weighted A-harmonic equations.
定义并研究了加权形式的A_调和方程的很弱解,很弱上解和很弱下解。