Periodic solutions of dissipative neutral differential systems with singular potential and P -Laplacian

In this paper, by using topological degree theory and some analysis skill, we consider the periodic solutions for the dissipative neutral differential systems with singular potential and p -Laplacian: ( ϕp ( x ′( t ) − μx ′( t − τ1 )))′ + \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\tfrac{d} {{dt}}$$ \end{document} grad G ( x ( t − τ2 )) = e ( t ). Sufficient conditions to guarantee the existence of periodic solution for the systems are obtained under having no restriction on the damping forces \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\tfrac{d} {{dt}}$$ \end{document} grad F ( x ).