一类抽象方程的解集的稳定性与本质连通区  

Stability of solutions to abstract equations and existence of essential components

作　　者：王湘美[1] 蒋佳[2] 

机构地区：[1]贵州大学理学院,贵州贵阳550025 [2]河北科技大学经济管理学院,河北石家庄050018

出　　处：《河北科技大学学报》2011年第6期524-528,535,共6页Journal of Hebei University of Science and Technology

基　　金：国家自然科学基金资助项目(61065010)

摘　　要：用集值分析的方法,讨论了抽象方程解集的稳定性,得到了通有稳定的结果,并给出了本质连通区存在的充分条件。讨论了抽象方程近似解集的稳定性,得到了通有稳定的结果,同时指出包含精确解的连通分支都是本质的,并且这样的连通分支只有有限个。最后作为应用,对非线性方程组的解集进行了讨论。By using the method of set-mapping, the stability of the solutions to abstract equations and the existence of essential components is studied. We derived that the solutions have Generic stability. At the same time, a sufficient condition is put for- ward that there is at least one essential component of the solutions when this condition is satisfied. It is derived that the proximal solutions also have generic stability; moreover, the components including exact solutions are essential, and the number of the components which include the exact solutions is finite. Then the stability of the solutions to system of nonlinear equations is analyzed, and a method is proposed to solve problems of system of the nonlinear equations.

关 键 词：集值映射 通有稳定性 连通分支 本质连通区 近似解 

分 类 号：O225[理学—运筹学与控制论]