An exact expression of positive periodic solution for a first-order singular equation

Advances in Difference Equations

Yun Xin¹  Jie Liu²  Xiaoxiao Cui² 

[1] College of Computer Science and Technology, Henan Polytechnic University, 454000, Jiaozuo, China;School of Mathematics and Information Science, Henan Polytechnic University, 454000, Jiaozuo, China;

关键词: First-order singular differential equation;    Attractive and repulsive singularities;    Indefinite singularity;    Positive periodic solution;    34B16;    34B18;    34C25;   

DOI  :  10.1186/s13662-020-02986-2

来源: Springer

【 摘 要 】

The main purpose of this paper is to obtain an exact expression of the positive periodic solution for a first-order differential equation with attractive and repulsive singularities. Moreover, we prove the existence of at least one positive periodic solution for this equation with an indefinite singularity by applications of topological degree theorem, and give the upper and lower bounds of the positive periodic solution.

【 授权许可】

CC BY