算子方程

It is proved that the problem has a global solution whose limit at infinity solves the original equation.

本文讨论解算子与右端数据均有扰动的半正定算子方程的动态系统方法。

In chapter 1, firstly, by using classical analysis methods, such as the introduction of Bessel function and semigroup theory, we transform the pseudo-parabolic equation into an abstract operator equation and achieve the existence and uniqueness of the local solution.

在第一章中，利用经典的分析方法，引入Bessel势函数，将伪抛物型方程转化为抽象算子方程，首先，利用算子半群理论，论证了局部解的存在唯一性。

In this article, we study the solutions of several operator equations and the stability of operator equations and inequalities.

本文研究了几类算子方程的解与算子方程和不等式的稳定性问题。

This method was mainly built on the operator matrix's singular value decomposition in the first class of operator equations, and then the best regularization parameters were selected in accordance with the characteristics of singular value so as to identify filter function, thereby removing noise of the function.

该方法主要建立在第一类算子方程的算子矩阵进行奇异值分解的基础上，然后根据奇异值的特征选取最佳正则化参数确定滤子函数，从而达到对该类函数的噪声去除效果。

We know that asymptotically linear operator equations have negative solutions and sign-changing solutions besides positive solutions, in this chapter, we obtain the existence of this three kind of solutions in Banach space, and we can know the concrete place of these solutions.

第三章的目的就在于借助于不动点指数理论利用一致正条件讨论非线性算子方程变号解的存在性，同时研究了变号解与一对正负解之间的关系，在一定条件下我们证明了：若算子方程x=Ax存在一个变号解，则它的正解和负解必定成对出现。

We know that cone theory is a kind of important method for the study of solutions for nonlinear operator equations.

本章进一步将—条件应用到抽象的算子方程中，得到了一类超线性算子方程的多解性。

Then we can turn the existence of periodic solution of this class of equations into the solvability of a operator equation.

再由这类方程的特点构造H→H的算子，将求周期解问题转化为求算子方程问题。

A new class of regularizing filter s is applied to solve the first kind of opertor equation.

借助紧算子的奇异系数，提出一族新的正则化子，从而建立了一类新的求解第一类算子方程的正则化方法。

By using the cone theory and the coupling upper and lower solution method, it is studied the existence uniqueness of solutions of nonlinear binary operator equations without monotone and continuity and compactness conditionsin Banach spaces.

利用锥和耦合上下解方法，研究Banach空间不具有单调性、连续性和紧性条件的非线性二元算子方程解的存在唯一性，并给出了迭代序列收敛於解的误差估计，所得结果改进和推广了混合单调算子方程的某些已知相应结果。

By using the cone theory and the coupling upper and lower solution method,it is studied the existence uniqueness of solutions of nonlinear binary operator equations without monotone and continuity and compactness conditionsin Banach spaces.

利用锥和耦合上下解方法，研究Banach空间不具有单调性、连续性和紧性条件的非线性二元算子方程解的存在唯一性，并给出了迭代序列收敛于解的误差估计，所得结果改进和推广了混合单调算子方程的某些已知相应结果。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。