Limit cycles and bounded trajectories for a nonlinear second-order differential equation

In this article, we determine the trajectories of maximum deviation, and the closed trajectories of maximum deviation for nonlinear differential equations of the form $$ ddot y+2a(t,y,dot y) dot y+b(t,y, dot y)y=c(t,y,dot y) $$ where the coefficients and the right-hand side are piecewise continuous functions in $t$ and continuous in $y,dot y$. Also we find necessary and sufficient conditions for the boundedness of all the trajectories.