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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (5): 690-696.doi: 10.3969/j.issn.1005-3085.2015.05.007

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一类二阶半线性系统周期解的存在性

周同藩   

  1. 西北师范大学商学院，兰州 730070
  • 收稿日期:2014-03-03 接受日期:2015-01-23 出版日期:2015-10-15 发布日期:2015-12-15

Existence of Periodic Solution for Semi-linear Second-order Differential Equations

ZHOU Tong-fan   

  1. College of Economics and Management, Northwest Normal University, Lanzhou 730070
  • Received:2014-03-03 Accepted:2015-01-23 Online:2015-10-15 Published:2015-12-15

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摘要： 本文研究一类二阶半线性微分方程周期解的存在性．关于这一课题的研究，传统方法的困难在于需要做大量细致的估计．我们利用偏微分方程粘性解理论的方法和经典的上、下解方法，结合Leray-Schauder不动点原理，在较弱的条件下证明了该系统周期解的存在性，这一结论改进并概括了以往关于绳索力学方程及近年来关于该系统的一些重要结果．

关键词: 半线性, 粘性解方法, 二阶微分方程, 周期解, 存在性

Abstract:

In this paper, we consider the existence of periodic solutions for a class of semi-linear second-order differential equations. The difficulty of traditional methods lies in a mass of detailed estimates. By applying the viscosity solutions method and the classical upper-lower solutions method, as well as the Leray-Schauder fixed point principle, we establish the existence of periodic solutions to the equation under some weaker conditions. Our result improves and generalizes many results on the ropes mechanics equations in the previous literature.

Key words: semi-linear, viscosity solutions method, second-order differential equation, periodic solution, existence

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