Periodic solutions for second order differential equations with indefinite singularities

Advances in Nonlinear Analysis

article

Shiping Lu¹  Xingchen Yu¹ 

[1] School of Mathematics and Statistics, Nanjing University of Information Science and Technology

关键词: Second order differential equation;    Continuation theorem;    Periodic solution;    Indefinite singularity;   

DOI  :  10.1515/anona-2020-0037

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

In this paper, the problem of periodic solutions is studied for second order differential equations with indefinite singularities x″(t)+f(x(t))x′(t)+φ(t)xm(t)−α(t)xμ(t)+β(t)xy(t)=0, $$\begin{array}{} \displaystyle x''(t)+ f(x(t))x'(t)+\varphi(t)x^m(t)-\frac{\alpha(t)}{x^\mu(t)}+\frac{\beta(t)}{x^y (t)}=0, \end{array}$$ where f ∈ C ((0, +∞), ℝ) may have a singularity at the origin, the signs of φ and α are allowed to change, m is a non-negative constant, μ and y are positive constants. The approach is based on a continuation theorem of Manásevich and Mawhin with techniques of a priori estimates.

【 授权许可】

CC BY