A new result on the existence of periodic solutions for Rayleigh equations with a singularity of repulsive type

作者：Chen, Lijuan^*; Lu, Shiping

来源：Advances in Difference Equations, 2017, 2017(1): 106.

DOI：10.1186/s13662-017-1136-z

• Rayleigh equation
• topological degree
• singularity
• periodic solution

In this paper, the problem of the existence of periodic solutions is studied for the second-order differential equations with a singularity of repulsive type,
x ''(t) + f(x'(t)) + phi(t)x(t) - 1/x'(t) = h(t),
where phi and h are T-periodic functions. By using topological degree theory, a new result on the existence of positive periodic solutions is obtained. The interesting thing is that the sign of the function phi(t) is allowed to be changed for t is an element of [0,T].

• 出版日期2017-4-8
• 单位南京信息工程大学