Periodic solution for p-Laplacian Rayleigh equation with attractive singularity and time-dependent deviating argument

In this paper, we consider a p-Laplacian singular Rayleigh equation with time-dependent deviating argument (φp(x′(t)))′+f(t,x′(t))+g(t,x(t−σ(t)))=e(t),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bigl(\varphi_{p}\bigl(x'(t)\bigr)\bigr)'+f \bigl(t,x'(t)\bigr)+g\bigl(t,x\bigl(t-\sigma(t)\bigr)\bigr)=e(t), $$\end{document} where g has an attractive singularity at x=0\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}. Using the Manásevich–Mawhin continuation theorem, we prove that the equation has at least one T-periodic solution.