偶数阶微分方程周期解的存在性  

Existence for Even Order Differential Equations

作　　者：黄涛[1] 胡桂开[1] 朱辉[1] 

机构地区：[1]东华理工大学数学与信息科学学院,江西抚州344000

出　　处：《东华理工大学学报（自然科学版）》2009年第3期298-300,共3页Journal of East China University of Technology(Natural Science)

基　　金：东华理工大学校长基金资助(DHXK0705)

摘　　要：讨论了高阶Duffing型微分方程周期解的存在性,此类方程是二阶Duffing型方程的推广,具有重要的理论意义。利用同胚延拓和不动点方法,构造处理了一类比文献所述条件更弱的Duffing型方程。通过构造一个先验界,利用Schaud-er不动点方法得到解的存在性结论,所使用的方法能广泛适用于各种边界条件。The existence of high order Duffing differential equation is discussed in this paper. The equation come from the two order Duffing differential equation. It has importance theories meaning. Author take homeomorphism extension and fixed point method structure processing this equation. This equation＇s condition is weaker. Struct- ing a boundary, we take Schauder fixed point method to get the result of existence. The result is new, and this method can apply to many boundary conditions.

关 键 词：同胚延拓 SOBOLEV空间 连续紧算子 

分 类 号：O175.1[理学—数学]