Mathematical Theory and Applications

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Positive Periodic Solutions for a Sixth-order Variable Coefficient Singular Differential Equation

Liu Jie, Li Panpan, Cheng Zhibo* ,Jing Taiyan   

  1. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China
  • About author:Cheng Zhibo; E-mail: czb_1982@126.com
  • Supported by:

    This work is partially supported by the Technological

    Innovation Talents in Universities and Colleges in Henan Province

    (No. 21HASTIT025), the Natural Science Foundation of Henan Province

    (No. 222300420449, 222300420171), the Key Research Funds for the Universities of Henan Province (No. 21A120005), the Innovative Research Team of Henan Polytechnic

    University (No. T2022-7), the Fundamental Research Funds for the Universities of Henan Provience (No. NSFRF220420) and the Foundation for Key Teacher by Henan Polytechnic University (No. 2022XQG-09).

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Abstract: In this paper, the existence of positive periodic solutions for a sixth-order singular differential equation is proved by the properties of Green function of a sixth-order linear differential equation with variable coefficient coupled with the Schauder's fixed point theorem. Our results contain both the attractive case and the repulsive case.

Key words: Singular differential equation, Green function, Positive periodic solution

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