摘要
目的研究迭代微分方程存在周期解的条件．方法采用变换定理和Ｓｃｈａｕｄｅｒ不动点原理证明周期解存在．结果建立了周期系数条件下多次迭代微分方程的存在周期解的定理．结论周期系数具有奇函数性且变量迭代有界时，周期解族布满全平面．
Aim To study the conditions for the existence of periodic solutions of a type of differential iterative equation. Methods The transform theorem and Schuder′s fixed point theorem were used. Results A theorem for the existence of periodic solutions of a multiple iteration equation with periodic coefficients is proved. Conclusion The family of periodic solutions covers the whole plane when the periodic coefficients show oddness and the iteration of variables possesses boundedness.
出处
《北京理工大学学报》
EI
CAS
CSCD
1999年第1期1-3,共3页
Transactions of Beijing Institute of Technology
基金
国家自然科学基金
高等学校博士学科点专项科研基金
关键词
迭代微分方程
变换定理
周期解
存在性
微分方程
differential iterative equation
fixed point
transform theorem
periodic solution
