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.
作者
姜黎鑫
丁卫
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)
出处
《西南师范大学学报（自然科学版）》
CAS
北大核心
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)
关键词
脉冲哈密顿系统
周期解
次线性
临界点
鞍点定理
impulsive Hamiltonian systems
periodic solutions
sublinear
critical points
saddle point theorem
