具有不定奇性的三阶微分方程周期正解的存在性  

Existence of Positive Periodic Solutions for a Third-Order Differential Equation with an Indefinite Singularity

作　　者：宋娟 程志波[1] 

机构地区：[1]河南理工大学数学与信息科学学院,河南 焦作

出　　处：《应用数学进展》2022年第11期7688-7695,共8页Advances in Applied Mathematics

摘　　要：不定奇性微分方程周期解的研究是微分方程中的一个重要组成部分,它在电子束模型、边界层理论和玻色–爱因斯坦凝聚体等多种学科中拥有广泛应用。近年来,许多研究关注的是排斥型三阶奇性微分方程周期正解的存在性问题。作为这一结果的延伸,本文讨论了一类具有不定奇性的三阶微分方程 周期正解的存在性,其中M是正常数,并且对任意有e(t)>0。函数h(t)在[0,T]上可变号的。利用Krasnoselskiĭ’s-Guo不动点定理和一些分析方法,我们证明该方程至少存在一个T-周期正解。The study of periodic solutions of indefinite singular differential equations is an important part of differential equations which has a wide range of applications in a variety of disciplines such as elec-tron beam focusing model, boundary layer theory and Bose-Einstein condensates. In recent years, much research has been concerned with the existence of positive periodic solutions of third-order differential equations with a repulsive singularity. As an extension of this result, in this paper, we consider the existence of positive periodic solutions to a class of third-order differential equation with an indefinite singularity ,where M is a real constant and M>0, and is a positive. The weight function h(t) is allowed to change signon [0,T]. By using Krasnoselskiĭ’s-Guo fixed point theorem and some analysis skills, sufficient conditions for the existence of at least one positive periodic solu-tion of this equation are established.

关 键 词：周期正解 不定奇性 Krasnoselski?'s-Guo不动点定理 三阶微分方程 

分 类 号：O175[理学—数学]