A new result on the existence of periodic solutions for Rayleigh equation with a singularity

作者：Guo, Yuanzhi^*; Wang, Yajiao; Zhou, Dongxue

来源：Advances in Difference Equations, 2017, 2017(1): 394.

DOI：10.1186/s13662-017-1449-y

• second order differential equation
• continuation theorem
• singularity
• periodic solution

In this paper, we study the existence of periodic solutions for Rayleigh equation with a singularity of repulsive type
x ''(t) + f(x'(t)) + phi(t)x(t) - 1/x(alpha)(t) = p (t),
where is a constant, and phi and p are T-periodic functions. The proof of the main result relies on a known continuation theorem of coincidence degree theory. The interesting point is that the sign of the function is allowed to change for .

• 出版日期2017-12-22
• 单位南京信息工程大学