| Volume 10, Number 4, 2020, Pages 1636-1650 DOI：10.11948/20190305 |
| Positive periodic solution for second-order nonlinear differential equation with singularity of attractive type |
| Jie Liu,Zhibo Cheng,Yi Wang |
| Keywords:Positive periodic solutions, singularity of attractive type, attractive-repulsive singularities. |
| Abstract: |
| This paper is devoted to
investigate the following second-order nonlinear differential
equation with singularity of attractive type
$$
x''-a(t)x=f(t,x)+e(t),
$$
where the nonlinear term $f$ has a singularity at the origin. By
using the Green''s function of the linear differential equation with
constant coefficient and Schauder''s fixed point theorem, we
establish some existence results of positive periodic solutions. |
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