精品文档---下载后可任意编辑Banach 空间上下半连续函数的线性扰动 P-S 条件的开题报告【摘要】本文主要讨论 Banach 空间上下半连续函数的线性扰动和 P-S 条件的关系。本文首先介绍了 Banach 空间和下半连续函数的相关概念和定义，并给出了一些常用的性质和定理。然后介绍了线性扰动的概念和定义，以及其在函数讨论中的应用。接着，引入了 P-S 条件的概念和定义，阐述了其在函数讨论中的重要性。同时，本文还给出了 P-S 条件的一些等价形式。最后，探讨了线性扰动和 P-S 条件之间的关系，并给出了一些有关的定理和结论。【关键词】Banach 空间；下半连续函数；线性扰动；P-S 条件；等价性；定理【Abstract】This paper mainly studies the relationship between linear perturbations and P-S conditions for lower semi-continuous functions on Banach spaces. This paper first introduces the relevant concepts and definitions of Banach spaces and lower semi-continuous functions, and gives some common properties and theorems. Then, the concept and definition of linear perturbation are introduced, as well as its application in function research. Subsequently, the concept and definition of P-S condition are introduced, and its importance in function research is expounded. At the same time, this paper also gives some equivalent forms of P-S conditions. Finally, the relationship between linear perturbation and P-S conditions is explored, and some relevant theorems and conclusions are given.【Key words】Banach space; lower semi-continuous function; linear perturbation; P-S condition; equivalence; theorem
