Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 133, pp. 1-9.

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

Author: Henry Gonzalez (Obuda Univ., Hungary)

Abstract:
 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.

Submitted April 15, 2011. Published October 13, 2011.
Math Subject Classifications: 34C05, 70K05.
Key Words: Ordinary differential equations; phase plane analysis; 
           limit cycles; maximum deviation trajectories.