摘要
2k阶微分方程周期解的存在和唯一性问题始终是学者们研究和探讨的一个重要课题。论文利用吸引盆理论和非负强制函数研究了Banach空间的全局同胚问题并应用于非线性方程,证明了2k阶微分方程周期解存在的充分条件,并证明相关文献中的结论是论文主要定理的推论.
An important problem in the existence and uniqueness of 2 π-periodic solution for 2k th order differential equations with resonance had been extensively investigated by many authors.The basin of attraction and the nonnegative coercive function were the main tool of our explosion in discussing the global diffeomorphism between Banach spaces,a new set of sufficient conditions was obtained in studying the existence and uniqueness of 2kth order differential equations with resonance.The result of this paper generalized the other paper’s conclusion and made it as a corollary.
出处
《安徽大学学报（自然科学版）》
CAS
北大核心
2011年第1期10-14,共5页
Journal of Anhui University(Natural Science Edition)
基金
Supported by the National Natural Science Foundation of China(20710015)
the Natural Science Foundation of Jiangsu(YW06037)
the Natural Science Foundation of Changzhou Institute of Technology(YN09090)
关键词
非负强制函数
吸引盆
全局同胚
周期解
共振
a nonnegative coercive function
the basin of attraction
homeomorphism
periodic solution
resonance
