An upper estimate for the number of limit cycles of even-degree Liénard equations in the focus case

We give an upper estimate for the number of limit cycles of the Liénard equations \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \dot{x} $\end{document} = y − F(x), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \dot{y} $\end{document} = −x of even degree in the case where its unique singular point (0, 0) is a focus.