在此基础之上，证明了方程的解集构成L的凸子格。
Based on the discussions, it was proved that the solution sets of the equations are convex sublattices of l.
但若故障支路形成回路或割集时，则仍需要解一组非线性方程，不过它的变量个数已大大减少。
But if there have some loops or cut sets between these fault branches, solving a set of nonlinear equations is also necessary, though the number of variables is much decreased.
由于集值算子在现代数学的广泛应用，本文还研讨了关于集值算子方程解的存在性；
Due to the wide applications of setvalued operators in modern mathematics, the solvability of the setvalued operator equations are studied.
本文提出了几个新概念，研究了1集压缩型随机算子方程的随机解。
In this paper, we introduce some new concepts, and study random solution of random operator equation of 1 set contractive type.
提出了1 -集压缩型随机算子方程耦合解的概念，并研究了这类随机算子方程耦合解的存在性。
In this paper, to 1-set contraction random operator equation, the author explained the conception of couple solution, obtained existence theorem of couple solution.
特别地，对紧支集小初值的情况，给出了经典解的生命区间及其在非线性波动方程中的应用。
In particular, for the case of small initial data with compact support, the author gives the life-span of classical solutions and its application to nonlinear wave equations.
主要运用能量方法及稳定集和不稳定集的观点，研究一类半线性抛物方程的整体解和局部解的存在性及爆破问题。
In this paper, we are concerned with the existence of global solutions or local solutions and blowup of one kind of semilinear heat equation.
基于平均方程，得到了参数平面上的转迁集，这些转迁集将参数平面划分为不同的区域，在各个不同的区域对应于系统不同的解。
Based on the averaged equation, the transition boundaries are sought to divide the parameter plane into different regions, corresponding to different types of the solutions.
用孤立不变集和孤立块的概念，给出了含一个参数的二阶常微分方程组的非驻定有界解分支点的存在性准则。
Using concepts of invariable set and isolated cube, we obtained existence for bifurcate points of bounded solutions of second order ordinary differential systems including a parameter.
有关的问题与概念有：凸算子，互易集与互易原理，H广义解，算子微分方程等。
Related problems and concepts include; convex operator, reciprocity set and reciprocity principles, H-generalized solution and operator-differential equation, etc.
特别当方程的初值问题的解不唯一时，研究解集的结构具有重要的意义。
It is very important to study the structure of solution set especially when the solution of the initial value problem of equations is not a single one.
在一般的假设条件下 ，我们应用性能势的基本性质直接建立了无限时间水平平均代价模型的最优性方程 ，并且证明了在紧致集上最优解的存在性 。
Under a general assumption, we establish directly the optimality equation for infinite time horizon average cost model and prove the existence of optimal solution in a compact action set by using p.
在一般的假设条件下 ，我们应用性能势的基本性质直接建立了无限时间水平平均代价模型的最优性方程 ，并且证明了在紧致集上最优解的存在性 。
Under a general assumption, we establish directly the optimality equation for infinite time horizon average cost model and prove the existence of optimal solution in a compact action set by using p.
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