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In this paper, the problem of the existence of a periodic solution is studied for the second order differential equation with a singularity of repulsive type    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$x''(t)+f\bigl(x(t)\bigr)x'(t)-g\bigl(x(t) \bigr)+\varphi(t)x(t)=h(t), $$\end{document}    x  ″   (  t  )  +  f   (  x  (  t  )  )    x  ′   (  t  )  −  g   (  x  (  t  )  )   +  φ  (  t  )  x  (  t  )  =  h  (  t  )  ,where    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$g(x)$\end{document}   g  (  x  )is singular at    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$x=0$\end{document}   x  =  0,  φ  and  h  are  T -periodic functions. By using the continuation theorem of Manásevich and Mawhin, a new result on the existence of positive periodic solution is obtained. It is interesting that the sign of the function    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$\varphi(t)$\end{document}   φ  (  t  )is allowed to change for    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$t\in[0,T]$\end{document}   t  ∈  [  0  ,  T  ].

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