二阶微分方程周期解的存在性和唯一性  

Existence and Uniqueness of Periodic Solutions for Second Order Differential Equations

作　　者：魏元鸿[1] 刘冬[2] 

机构地区：[1]吉林大学数学研究所,长春130012 [2]吉林大学数学学院,长春130012

出　　处：《吉林大学学报（理学版）》2010年第2期229-230,共2页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:J0630104)

摘　　要：应用Schauder不动点定理研究二阶微分方程周期解的存在性和唯一性,在右端函数连续可微时,得到了周期解的存在性和唯一性,并对右端函数仅为连续的情形给出了周期解存在的充分条件.The periodic solutions for second order differential equations were investigated by means of the Schauder＇ s fixed point theorem. The existence and uniqueness of periodic solutions are established when the function f（t,x,x＇） is continuously differentiable. Furthermore, under the condition that the right-hand function is only continuous, we have established the sufficient conditions for the existence of periodic solutions.

关 键 词：周期解 SCHAUDER不动点定理 存在性 唯一性 

分 类 号：O175.14[理学—数学]