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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.