Global Asymptotic Stability for Oscillators with Superlinear Damping

A necessary and sufficient condition is established for the equilibrium of the damped superlinear oscillator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x^{\prime\prime} + a(t)\phi_q(x^{\prime}) + \omega^2x = 0$$\end{document}