反序上下解条件下周期边值问题的唯一解  

The unique solution for periodic differential equations with upper and lower solutions in reverse order

作　　者：杨爱军[1] 王河林[1] 

机构地区：[1]浙江工业大学理学院,浙江杭州310023

出　　处：《浙江工业大学学报》2013年第6期690-694,共5页Journal of Zhejiang University of Technology

基　　金：国家自然科学基金资助项目(11226148;61273016);浙江省自然科学基金资助项目(LY12F05006)

摘　　要：通过建立一个具有有界解的辅助周期系统,详细研究了一类常微分方程的周期边值问题,得到了方程解的存在唯一性结论.研究过程中,针对所建立的辅助系统,首先运用逆序上下解方法和反极大值原理,巧妙地建立了单调迭代序列,进而得到了辅助系统的一组极值解,然后根据辅助系统的极值解,给出了所讨论的周期问题的解的一个估计,最后结合相关理论,文章给出一个具体实例,通过实例很好的说明了该方法的巧妙之处,更重要的是,提出的方法能用来解决其它类型的周期边值问题.This paper discussed a kind of periodic problem and obtained the existence of the unique solution of the considered periodic problem by constructing an auxiliary system with bounded solutions. The reversed order upper and lower solution method and an anti-maximum principle are employed to establish the monotone iterative sequences and obtain the extremal solutions for the auxiliary system. In addition, the extremal solutions of the auxiliary system can give an estimate of the solution of the discussed periodic problem. Furthermore, combining with the related theories, an example is given to illustrate the results, and the method proposed here can be used to discuss the similar problems.

关 键 词：反序上下解 反极大值原理 单调迭代方法 唯一解 

分 类 号：O175.1[理学—数学]