Electron. J. Diff. Equ., Vol. 2011 (2011), No. 133, pp. 1-9.

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

Henry Gonzalez

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.

Show me the PDF file (292 KB), TEX file, and other files for this article.

Henry González
Faculty of Light Industry and Environmental Protection Engineering
Obuda University
1034 Budapest, Bécsi út 96/B, Hungary
email: gonzalez.henry@rkk.uni-obuda.hu

Return to the EJDE web page