非自治二阶系统解存在性的一些充分条件  

Sufficient Conditions for the Existence of a Solution for the Non-autonomous Second-order System

作　　者：潘文秀[1] 

机构地区：[1]钦州学院数学与计算机科学学院,广西钦州535000

出　　处：《内江师范学院学报》2012年第10期8-10,共3页Journal of Neijiang Normal University

基　　金：钦州学院校级立项项目(2011XJKY-35C);钦州学院校级立项项目(2011XJKY-16B)

摘　　要：利用鞍点归约方法及极大极小方法,通过对空间进行分解,在子空间上寻找关于非自治二阶系统的解.根据子空间的特殊性,在子空间上寻找极值点,通过映射得到全空间上的极值点,从而寻找相对较弱的解的存在性条件.这样在梯度函数满足线性增长条件或单调条件下,得到了关于非自治二阶系统解的存在性方面的一些新的充分性条件.By aid of saddle point reduction method and minimax method and through decomposition of space, an effort is made to find the solution of non-autonomous second-order system in the sub-spaces. Based on the peculiarity of the sub-spaces, the extreme point is located and by means of mapping, the extreme point in the total space is worked out, so as to find out the existential conditions for a relatively weaker solution of the system. Therefore, when a gradient function meets the condition of linear growth or monotone condition, some new sufficient conditions for the existence of a solution are thus obtained for the non-autonomous second-order system.

关 键 词：鞍点归约 非自治二阶系统 极大极小方法 强制性 

分 类 号：O157.1[理学—数学]