Advances in Nonlinear Analysis | |
Periodic solutions for second order differential equations with indefinite singularities | |
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
【 预 览 】
Files | Size | Format | View |
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RO202107200000583ZK.pdf | 378KB | download |