弱次线性增长条件下脉冲系统的周期解  

Periodic Solutions of Impulsive System Under Weak Sublinear Growth Conditions

作　　者：姜黎鑫[1,2] 丁卫[1] 

机构地区：[1]南通大学理学院,江苏南通226019 [2]南通师范高等专科学校数理系,江苏南通226006

出　　处：《南通大学学报（自然科学版）》2016年第1期85-90,共6页Journal of Nantong University(Natural Science Edition)　

基　　金：国家自然科学基金项目(11501308)

摘　　要：主要研究了带阻尼项的脉冲方程在弱的次线性增长的条件下周期解的存在性问题.首先证明该系统的周期解对应着一个泛函的临界点,从而将周期解的存在性问题转化为寻找该泛函的临界点问题.然后,在弱的次线性条件下,利用鞍点定理,证明了临界点的存在性,从而得到了带阻尼项的脉冲方程在弱的次线性增长的条件下至少存在一个周期解.In this study the existence of periodic solutions of impulsive systems was probed with damped term under weak sublinear growth conditions. Firstly the result that the periodic solutions of this system corresponding to the critical points of a functional was proved, and thus the existence problem of periodic solutions was transformed to find the critical points of the functional. The existence of critical points was proved by using the Saddle Point Theorem under the conditions of weak linear growth, that is, there exists at least one periodic solution of the above impulsive systems.

关 键 词：弱次线性条件 脉冲 周期解 临界点 鞍点定理 

分 类 号：O193[理学—数学]