摘要
通过临界点理论和Z2不变群指标理论,证得I(x)有无穷多个临界点,再由变分原理可得方程(2)与方程(3)等价,在改变条件的情况下,得出了一在二阶泛函微分方程存在无穷多个周期解.
By critical point and Z2-group index theory, the functional l(z) posesses infinite critical points and equation (2) is equivalent to equation (3) by the variational structure. In the changed conditions, we obtain infinite periodic solutions to a class of second-order differential equations (c(t)x'(t-x))'+f(t,x(t),x(t-r),x(t-2r))=0.
出处
《安徽师范大学学报(自然科学版)》
CAS
北大核心
2010年第1期5-10,共6页
Journal of Anhui Normal University(Natural Science)
基金
Sponsored by the key NSF of Education Ministry of China(207047)
关键词
变分结构
Z2不变指标群理论
临界点
周期解
variational structure
Z2- group index theory
critical points
periodic solutions