华东师范大学学报(自然科学版) ›› 2006, Vol. 2006 ›› Issue (1): 40-44,1.

• 数学 统计学 • 上一篇    下一篇

一类共振二阶系统的多重周期解

孟海霞1, 郭晓峰2   

  1. 1. 兰州交通大学 数理学院, 兰州 730070;2. 西安电子科技大学 应用数学系, 西安 710071
  • 收稿日期:2004-09-20 修回日期:2005-01-19 出版日期:2006-01-25 发布日期:2006-01-25
  • 通讯作者: 孟海霞

Multi-periodic Solutions for A Class of Resonance Second Order Systems(Chinese)

MENG Hai-xia1, GUO Xiao-feng2   

  1. 1. College of Mathematics and Physics , Lanzhou Jiaotong University, Lanzhou 730070, China; 2. Department of Applied Mathematics , Xidian University , Xi'an 710071, China
  • Received:2004-09-20 Revised:2005-01-19 Online:2006-01-25 Published:2006-01-25
  • Contact: MENG Hai-xia

摘要： 利用Z2型山路定理,获得关于形如ü(t)+k2ω2u+▽F(t,u(t))=0(a．e．t∈[0,T])的超二次共振非自治二阶系统,当无界时,多重周期解存在性的定理．

关键词: 二阶系统, 共振, 超二次, 非自治, 周期解, 临界点, 二阶系统, 共振, 超二次, 非自治, 周期解, 临界点

Abstract: The existence and multiplicity of periodic solutions are obtained for a class of su-perquadratic resonance nonautonomous second order systems ü(t)+k2ω2u+▽F(t, u(t)) = 0, a.e.t ∈ [0,T] by Z2 version of the Mountain Pass Theorem on the condition that is unbounded.

Key words: resonance, superquadratic, Z2 version of the Mountain Pass Theorem, nonautonomous, periodic solution, critical point, second order systems, resonance, superquadratic, Z2 version of the Mountain Pass Theorem, nonautonomous, periodic solution, critical point

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