一般次线性条件下脉冲方程的周期解  

Periodic Solutions of Generalized Sublinear Impulsive Hamiltonian Systems

作　　者：姜黎鑫[1] 丁卫[2] JIANG Li-xin;DING Wei(Department Mathematics and Physics,Nantong Normal College,Nantong Jiangsu 226006,China;School of Sciences,Nantong University,Nantong Jiangsu 226007,China)

机构地区：[1]南通师范高等专科学校数理系,江苏南通226006 [2]南通大学理学院,江苏南通226007

出　　处：《西南师范大学学报（自然科学版）》2018年第11期18-23,共6页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11501308)

摘　　要：次线性条件下,脉冲系统x"+f(t,x)=0,a.e.t∈[0,2π]Δx'(t_j):=x'(t+j)-x'(t_j^-)=I_j(x(t_j))j=1,2,…,p的周期解的存在性被广泛研究.这里的次线性主要体现在f(t,x)被下面次线性函数控制:|f(t,x)|≤g(t)|x|α+h(t)其中g,h∈L^1(0,2π;R^+),α∈[0,1).本文减弱了上述次线性控制的要求,利用临界点理论证明了当f(t,x)满足某个函数类条件时,脉冲方程周期解是存在的,从而推广了相关结果.Under sublinear conditions,the periodic solutions of impulsive Hamiltonian systems x″+f(t,x)=0,a.e.t∈[0,2π]Δx′(t j):=x′(t+j)-x′(t-j)=I j(x(t j)) j=1,2,…,p have been studied extensively.Here Sublinearity is reflected in controlled function of f(t,x):|f(t,x)|≤g(t)|x|α+h(t)where g,h∈L 1(0,2π;R+),α∈[0,1).In this paper,we weaken sublinear conditions and prove the existence of periodic solutions for impulsive Hamiltonian systems if f(t,x)belongs to some function set by critical point theory.This generalizes known results.

关 键 词：脉冲哈密顿系统 周期解 次线性 临界点 鞍点定理 

分 类 号：O175[理学—数学]