| 非自治二阶系统解存在性的一些充分条件 |
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| 引用本文： | 潘文秀. 非自治二阶系统解存在性的一些充分条件[J]. 内江师范学院学报, 2012, 27(10): 8-10 |
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| 作者姓名： | 潘文秀 |
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| 作者单位： | 钦州学院数学与计算机科学学院,广西 钦州,535000 |
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| 基金项目： | 钦州学院校级立项项目(2011XJKY-35C);钦州学院校级立项项目(2011XJKY-16B) |
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| 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.
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| 关 键 词： | 鞍点归约 非自治二阶系统 极大极小方法 强制性 |
Sufficient Conditions for the Existence of a Solution for the Non-autonomous Second-order System |
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| PAN Wen-xiu. Sufficient Conditions for the Existence of a Solution for the Non-autonomous Second-order System[J]. Journal of Neijiang Teachers College, 2012, 27(10): 8-10 |
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| Authors: | PAN Wen-xiu |
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| Affiliation: | PAN Wen-xiu(College of Mathematics & Computer Science,Qinzhou University,Qinzhou,Guangxi 535000,China) |
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| Abstract: | 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. |
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| Keywords: | saddle point reduction method the non-autonomous second-order system min-max method coerciveness |
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