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《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (8): 33-41.doi: 10.6040/j.issn.1671-9352.0.2018.707

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带阻尼项的二阶奇异微分方程的正周期解

陈瑞鹏,李小亚   

  1. 北方民族大学数学与信息科学学院, 宁夏 银川 750021
  • 出版日期:2019-08-20 发布日期:2019-07-03
  • 作者简介:陈瑞鹏(1986— ), 男, 博士, 讲师, 研究方向为微分方程与动力系统. E-mail:ruipengchen@126.com
  • 基金资助:
    国家自然科学基金资助项目(11701012);北方民族大学重大专项资助项目(ZDZX201804);宁夏高等教育一流学科建设资助项目(NXYLXK2017B09)

Positive periodic solutions for second-order singular differential equations with damping terms

CHEN Rui-peng, LI Xiao-ya   

  1. College of Mathematics and Information Science, North Minzu University, Yinchuan 750021, Ningxia, China
  • Online:2019-08-20 Published:2019-07-03

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摘要： 研究带阻尼项的二阶微分方程u″+p(t)u'+q(t)u=f(t,u)+c(t)正周期解的存在性, 其中 p,q,c∈L1(R/TZ;R), f为Carathéodory函数且在u=0处具有奇异性。运用不动点理论, 为该方程建立了若干正周期解的存在性结果, 所得结果推广并改进了已有文献的相关结论。

关键词: 正周期解, 存在性, 奇性, 不动点理论

Abstract: This paper studies the existence of positive periodic solutions of u″+p(t)u'+q(t)u=f(t,u)+c(t), where p,q,c∈L1(R/TZ;R), f is a Carathéodory function and is singular when u=0. By means of the fixed point theory, several existence theorems are established for the above equation, and some recent results in the literature are generalized and improved.

Key words: positive periodic solution, existence, singularity, fixed point theory

中图分类号: 

  • O175.8
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