KKM理论是非线性分析中重要的研究内容之一，它在平衡问题、最优化问题、相辅相成问题等方面具有广泛的应用。 自1929年，KKM原理出世以来，很多学者都在探索在特定的空间上建立最佳的KKM型定理，以便解决非线性分析中的各类问题，并取得一系列重要成果，大大推广和改进了KKM理论。 本课题拟在没有线性结构的非紧致框架的抽象拓扑空间上利用KKM原理建立广泛意义的KKM型定理和全交定理，并以此为理论根据讨论不动点问题、重合点问题、截口问题、极大极小问题等；进一步，作为应用，讨论广义变分不等式的解的存在性问题、双边有界不等式解的存在性问题、平衡点存在问题、相辅相成问题等，使KKM理论在一般拓扑空间上得到充分的补充、发展和完善。与此同时，本课题的研究将对边疆少数民族地区的数学教育人才的培养以及数学学科的发展具有积极的意义。

As an important research branch in nonlinear analysis , the KKM theory is widely applied in the research of equilibium problems, optimization problems and mutul benefit problems and so on. Since KKM principle was first introduced in 1929, many researchers have tried to solve various problems in nonlinear analysis by formulating the optimum KKM theories on the certain spaces, resulting in a series of important achienements wich improved KKM theory sustancially. In this paropram, our goal is to apply the KKM principle to formulate general KKM theroems and intersection theorems on non-compact framed abstract topological spaces without linear construction. Based on these results, we will esplore fixed point problems, section problems and minimax inequality problems. As applications, we will discuss the existence of solutions of generalized varivational inequilities, two-side bounded ineuqlities, equlibium problems and mutul benefit problem and so on. Also, we expect this program to have a positive effect on the development of mathematics research and education at minority regions.