一般次线性条件下脉冲方程的周期解

姜黎鑫<sup>1</sup>,丁卫<sup>2</sup>

doi:10.13718/j.cnki.xsxb.2018.11.004

西南师范大学学报(自然科学版)

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一般次线性条件下脉冲方程的周期解

姜黎鑫1,丁卫2. 一般次线性条件下脉冲方程的周期解[J]. 西南师范大学学报(自然科学版), 2018, 43(11): 18-23. doi: 10.13718/j.cnki.xsxb.2018.11.004

引用本文:

姜黎鑫¹,丁卫². 一般次线性条件下脉冲方程的周期解[J]. 西南师范大学学报(自然科学版), 2018, 43(11): 18-23. doi: 10.13718/j.cnki.xsxb.2018.11.004

JIANG Li-xin1, DING Wei2. Periodic Solutions of Generalized Sublinear Impulsive Hamiltonian Systems[J]. Journal of Southwest China Normal University(Natural Science Edition), 2018, 43(11): 18-23. doi: 10.13718/j.cnki.xsxb.2018.11.004

Citation:

JIANG Li-xin¹, DING Wei². Periodic Solutions of Generalized Sublinear Impulsive Hamiltonian Systems[J]. Journal of Southwest China Normal University(Natural Science Edition), 2018, 43(11): 18-23. doi: 10.13718/j.cnki.xsxb.2018.11.004

一般次线性条件下脉冲方程的周期解

姜黎鑫¹,丁卫²

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

Periodic Solutions of Generalized Sublinear Impulsive Hamiltonian Systems

JIANG Li-xin¹, DING Wei²

1. Department Mathematics and Physics, Nantong Normal College, Nantong Jiangsu 226006, China;
2. School of Sciences, Nantong University, Nantong Jiangsu 226007, China

摘要: 次线性条件下，脉冲系统x″+f（t，x）=0，a.e.t∈[0，2π]Δx'（tj）：=x'（tj+）-x'（tj-）=Ij（x（tj））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∈L1（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.
- 脉冲哈密顿系统 /
- 周期解 /
- 次线性 /
- 临界点 /
- 鞍点定理
Abstract: Under sublinear conditions, the periodic solutions of impulsive Hamiltonian systemsx″+f(t, x)=0, a.e.t∈[0, 2π]Δx'(tj):=x'(tj+)-x'(tj-)=Ij(x(tj)) j=1,2,…,phave 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∈L1(0,2π;R+),α∈[0, 1). In this paper, we weaken sublinear conditions and prove the existence of periodic solutions forimpulsive Hamiltonian systems if f(t, x) belongs to some function set by critical point theory. This generalizes known results.
- impulsive Hamiltonian systems /
- periodic solutions /
- sublinear /
- critical points /
- saddle point theorem .

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一般次线性条件下脉冲方程的周期解

姜黎鑫¹,丁卫²

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

收稿日期: 2017-10-30

关键词:

摘要: 次线性条件下，脉冲系统x″+f（t，x）=0，a.e.t∈[0，2π]Δx'（tj）：=x'（tj+）-x'（tj-）=Ij（x（tj））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∈L1（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.